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Tsukasa Iwabuchi

Section

Graduate School of Science

Job title

Associate Professor

Degree

博士（理学）（東北大学）
修士（理学）（東北大学）

researchmap

https://researchmap.jp/7000019093

J-GLOBAL ID

201101092354782438

Research History 6

2016/10 - Present

東北大学大学院理学研究科　准教授
2015/04 - 2016/09

大阪市立大学大学院理学研究科　准教授
2012/04 - 2015/03

中央大学理工学部　助教
2011/04 - 2012/03

Tohoku University　Graduate School of Science
2008/04 - 2011/03

Ichinoseki National College of Technology
Tohoku University Graduate School of Science, Department of Mathematics, Analysis　Assistant Professor

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Education 4

Tohoku University

- 2011
Tohoku University

- 2008
Tohoku University　Faculty of Science　Department of Mathematics

- 2006
岩手県立一関第一高等学校

- 2002

Professional Memberships 1

The Mathematical Society of Japan

Research Interests 1

偏微分方程式

Research Areas 1

Natural sciences / Basic analysis / partial differential equations

Awards 1

日本数学会賞建部賢弘賞特別賞

2017/09　一般社団法人「日本数学会」

Papers 35

Optimal decay estimates for the radially symmetric compressible Navier-Stokes equations Peer-reviewed

Tsukasa Iwabuchi, Dáithí Ó hAodha

Journal of Differential Equations　441　113487-113487　2025/10
Publisher: Elsevier BV
DOI： 10.1016/j.jde.2025.113487 　

ISSN： 0022-0396
The derivative structure for a quadratic nonlinearity and uniqueness for SQG Peer-reviewed

Tsukasa Iwabuchi

Journal of Differential Equations　429　802-825　2025/06
Publisher: Elsevier BV
DOI： 10.1016/j.jde.2025.02.057 　

ISSN： 0022-0396
On the uniqueness of the mild solution of the critical quasi-geostrophic equation Peer-reviewed

Tsukasa Iwabuchi, Taiki Okazaki

Communications in Mathematical Sciences　23　(4)　935-946　2025
Publisher: International Press of Boston
DOI： 10.4310/cms.250412102118 　

ISSN： 1539-6746

eISSN： 1945-0796
Remark on the uniqueness of the mild solution of SQG equation Peer-reviewed

Tsukasa Iwabuchi, Ryoma Ueda

Partial Differential Equations and Applications　5　(5)　2024/09/11
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s42985-024-00301-2 　

ISSN： 2662-2963

eISSN： 2662-2971
Sobolev spaces on arbitrary domains and semigroups generated by the fractional Laplacian Peer-reviewed

Reinhard Farwig, Tsukasa Iwabuchi

Bulletin des Sciences Mathématiques　193　103440-103440　2024/07
Publisher: Elsevier BV
DOI： 10.1016/j.bulsci.2024.103440 　

ISSN： 0007-4497
Optimality of the Decay Estimate of Solutions to the Linearised Curl-Free Compressible Navier–Stokes Equations Peer-reviewed

Tsukasa Iwabuchi, Dáithí Ó hAodha

Journal of Mathematical Fluid Mechanics　26　(1)　2023/11/14
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00021-023-00837-0 　

ISSN： 1422-6928

eISSN： 1422-6952

More details Close

Abstract We discuss optimal estimates of solutions to the compressible Navier–Stokes equations in Besov norms. In particular, we consider the estimate of the curl-free part of the solution to the linearised equations, in the homogeneous case. We prove that our estimate is optimal in the $$L^\infty $$-norm by showing that the norm is bounded from below by the same decay rate.
The Leibniz rule for the Dirichlet and the Neumann Laplacian Peer-reviewed

Tsukasa Iwabuchi

Tohoku Mathematical Journal　75　(1)　67-88　2023/03/01
Publisher: Mathematical Institute, Tohoku University
DOI： 10.2748/tmj.20211112 　

ISSN： 0040-8735
Energy conservation law for weak solutions of the full compressible Navier-Stokes equations Peer-reviewed

Motofumi Aoki, Tsukasa Iwabuchi

Journal of Differential Equations　341　481-503　2022/12
Publisher: Elsevier BV
DOI： 10.1016/j.jde.2022.09.006 　

ISSN： 0022-0396
An application of spectral localization to the critical SQG on a ball Peer-reviewed

Tsukasa Iwabuchi

Journal of Evolution Equations　22　(4)　2022/12
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00028-022-00839-x 　

ISSN： 1424-3199

eISSN： 1424-3202
Large-time behaviour of solutions to the surface quasi-geostrophic equation Peer-reviewed

Dáithí Ó hAodha, Tsukasa Iwabuchi

Partial Differential Equations and Applications　3　(5)　2022/10
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s42985-022-00197-w 　

ISSN： 2662-2963

eISSN： 2662-2971
Ill-posedness for the compressible Navier–Stokes equations under barotropic condition in limiting Besov spaces Peer-reviewed

Tsukasa IWABUCHI, Takayoshi OGAWA

Journal of the Mathematical Society of Japan　74　(2)　2022/04/21
Publisher: Mathematical Society of Japan (Project Euclid)
DOI： 10.2969/jmsj/81598159 　

ISSN： 0025-5645
On analyticity up to the boundary for critical quasi-geostrophic equation in the half space Peer-reviewed

Tsukasa Iwabuchi

Communications on Pure and Applied Analysis　21　(4)　1209-1209　2022
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI： 10.3934/cpaa.2022016 　

ISSN： 1534-0392

eISSN： 1553-5258

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<p lang="fr"><p style='text-indent:20px;'>We study the Cauchy problem for the surface quasi-geostrophic equation with the critical dissipation in the two dimensional half space under the homogeneous Dirichlet boundary condition. We show the global existence, the uniqueness and the analyticity of solutions, and the real analyticity up to the boundary is obtained. We will show a natural ways to estimate the nonlinear term for functions satisfying the Dirichlet boundary condition.</p></p>
Ill-posedness for the Cauchy problem of the two-dimensional compressible Navier-Stokes equations for an ideal gas Peer-reviewed

Tsukasa Iwabuchi, Takayoshi Ogawa

Journal of Elliptic and Parabolic Equations　7　(2)　571-587　2021/12
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s41808-021-00136-7 　

ISSN： 2296-9020

eISSN： 2296-9039
Remark on smoothing property of weak solutions for the Navier-Stokes equations Peer-reviewed

M. Aoki, T. Iwabuchi

Differential Integral Equations　34　(3/4)　199-222　2021
Self-similar solutions of the compressible Navier-Stokes equations Peer-reviewed

P. Germain, T. Iwabuchi

Arch. Ration. Mech. Anal.　240　(3)　1645-1673　2021
On self-similar solutions to degenerate compressible Navier-Stokes equations Peer-reviewed

P. Germain, T. Iwabuchi, T. Léger

Communications in Mathematical Physics　381　(3)　1001-1030　2021
Backward self-similar solutions for compressible Navier-Stokes equations Peer-reviewed

P. Germain, T. Iwabuchi, T. Léger

Nonlinearity　34　(2)　868-893　2021
Bilinear estimates in Besov spaces generated by the Dirichlet Laplacian..[Journal of Mathematical Analysis and Applications Peer-reviewed

T. Iwabuchi, T. Matsuyama, K. Taniguchi

Journal of Mathematical Analysis and Applications　494　(2)　124640-124640　2021
Publisher: Elsevier BV
DOI： 10.1016/j.jmaa.2020.124640 　

ISSN： 0022-247X
Analyticity and large time behavior for the Burgers equation and the quasi-geostrophic equation, the both with the critical dissipation Peer-reviewed

T. Iwabuchi

Annales de l'Institut Henri Poincaré C, Analyse non linéaire　37　(4)　855-876　2020
Besov spaces on open sets Peer-reviewed

T. Iwabuchi, T. Matsuyama, K. Taniguchi

Bull. Sci. Math　152　93-149　2019
Publisher: Elsevier BV
DOI： 10.1016/j.bulsci.2019.01.008 　

ISSN： 0007-4497
Boundedness of spectral multipliers for Schrödinger operators on open sets Peer-reviewed

T. Iwabuchi, T. Matsuyama, K. Taniguchi

Rev. Mat. Iberoam　34　(3)　1277-1322　2018/08
The semigroup generated by the Dirichlet Laplacian of fractional order Peer-reviewed

Tsukasa Iwabuchi

Analysis and PDE　11　(3)　683-703　2018
Publisher: Mathematical Sciences Publishers
DOI： 10.2140/apde.2018.11.683 　

ISSN： 1948-206X 2157-5045
Existence of mild solutions for a Hamilton-Jacobi equation with critical fractional viscosity in the Besov spaces Peer-reviewed

Tsukasa Iwabuchi, Tatsuki Kawakami

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES　107　(4)　464-489　2017/04

DOI： 10.1016/j.matpur.2016.07.007 　

ISSN： 0021-7824

eISSN： 1776-3371
Global solutions for the incompressible rotating stably stratified fluids Peer-reviewed

Tsukasa Iwabuchi, Alex Mahalov, Ryo Takada

MATHEMATISCHE NACHRICHTEN　290　(4)　613-631　2017/03

DOI： 10.1002/mana.201500385 　

ISSN： 0025-584X

eISSN： 1522-2616
On the existence time of local solutions for critical semilinear Schrodinger equations in Sobolev spaces Peer-reviewed

Tsukasa Iwabuchi, Makoto Nakamura

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS　33　168-180　2017/02

DOI： 10.1016/j.nonrwa.2016.06.009 　

ISSN： 1468-1218
L p -boundedness of Functions of Schrödinger Operators on an Open Set of ℝ d $$\mathbb{R}^{d}$$

Tsukasa Iwabuchi, Tokio Matsuyama, Koichi Taniguchi

Trends in Mathematics　307-312　2017
Publisher: Springer International Publishing
DOI： 10.1007/978-3-319-48812-7_39 　

ISSN： 2297-0215

eISSN： 2297-024X
ILL-POSEDNESS ISSUE FOR THE DRIFT DIFFUSION SYSTEM IN THE HOMOGENEOUS BESOV SPACES Peer-reviewed

Tsukasa Iwabuchi, Takayoshi Ogawa

OSAKA JOURNAL OF MATHEMATICS　53　(4)　919-939　2016/10

ISSN： 0030-6126
Ill-posedness for a system of quadratic nonlinear Schrodinger equations in two dimensions Peer-reviewed

Tsukasa Iwabuchi, Takayoshi Ogawa, Kota Uriya

JOURNAL OF FUNCTIONAL ANALYSIS　271　(1)　136-163　2016/07

DOI： 10.1016/j.jfa.2016.04.017 　

ISSN： 0022-1236

eISSN： 1096-0783
Ill-posedness for the Cauchy problem of the non-linear Schr\"odinger system with mass resonance Peer-reviewed

T. Iwabuchi, T. Ogawa, K. Uriya

J. Functional Anal.　271　(1)　136-163　2016/05
Stability of time periodic solutions for the rotating navier-stokes equations Peer-reviewed

Tsukasa Iwabuchi, Alex Mahalov, Ryo Takada

Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday　none　321-335　2016
Publisher: Springer Verlag
DOI： 10.1007/978-3-0348-0939-9_17 　
Dispersive Effect of the Coriolis Force and the Local Well-Posedness for the Navier-Stokes Equations in the Rotational Framework Peer-reviewed

Tsukasa Iwabuchi, Ryo Takada

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA　58　(3)　365-385　2015/12

DOI： 10.1619/fesi.58.365 　

ISSN： 0532-8721
ILL-POSEDNESS FOR THE QUADRATIC NONLINEAR SCHRODINGER EQUATION WITH NONLINEARITY vertical bar u vertical bar(2) Peer-reviewed

Tsukasa Iwabuchi, Kota Uriya

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS　14　(4)　1395-1405　2015/07

DOI： 10.3934/cpaa.2015.14.1395 　

ISSN： 1534-0392

eISSN： 1553-5258
Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior Peer-reviewed

Tsukasa Iwabuchi

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE　32　(3)　687-713　2015/05

DOI： 10.1016/j.anihpc.2014.03.002 　

ISSN： 0294-1449

eISSN： 1873-1430
ILL-POSEDNESS FOR THE NONLINEAR SCHRODINGER EQUATION WITH QUADRATIC NON-LINEARITY IN LOW DIMENSIONS Peer-reviewed

Tsukasa Iwabuchi, Takayoshi Ogawa

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY　367　(4)　2613-2630　2015/04

DOI： 10.1090/S0002-9947-2014-06000-5 　

ISSN： 0002-9947

eISSN： 1088-6850
Global well-posedness for Keller-Segel system in Besov type spaces Peer-reviewed

Tsukasa Iwabuchi

Journal of Mathematical Analysis and Applications　379　(2)　930-948　2011/07/15

DOI： 10.1016/j.jmaa.2011.02.010 　

ISSN： 0022-247X 1096-0813

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Misc. 20

Remarks on the ill-posedness results for the drift diffusion system (Harmonic Analysis and Nonlinear Partial Differential Equations)

Iwabuchi Tsukasa, Ogawa Takayoshi

RIMS Kokyuroku Bessatsu　56　31-41　2016/04
Publisher: Kyoto University
ISSN： 1881-6193
ILL-POSEDNESS FOR THE NONLINEAR SCHRODINGIER [SCHRODINGER] EQUATIONS IN ONE SPACE DIMENSION (Regularity and Singularity for Geometric Partial Differential Equations and Conservation Laws)

Iwabuchi Tsukasa, Ogawa Takayoshi

RIMS Kokyuroku　1969　146-152　2015/11
Publisher: Kyoto University
ISSN： 1880-2818
Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type

Tsukasa Iwabuchi, Ryo Takada

JOURNAL OF FUNCTIONAL ANALYSIS　267　(5)　1321-1337　2014/09

DOI： 10.1016/j.jfa.2014.05.022 　

ISSN： 0022-1236

eISSN： 1096-0783
Local solvability of the Keller-Segel system with Cauchy data in the Besov spaces

Tsukasa Iwabuchi

MATHEMATICAL METHODS IN THE APPLIED SCIENCES　37　(9)　1273-1277　2014/06

DOI： 10.1002/mma.2883 　

ISSN： 0170-4214

eISSN： 1099-1476
Global solutions for the Navier-Stokes equations in the rotational framework

Tsukasa Iwabuchi, Ryo Takada

MATHEMATISCHE ANNALEN　357　(2)　727-741　2013/10

DOI： 10.1007/s00208-013-0923-4 　

ISSN： 0025-5831
Dispersive effect of the Coriolis force for the Navier-Stokes equations in the rotational framework (Harmonic Analysis and Nonlinear Partial Differential Equations)

Iwabuchi Tsukasa, Takada Ryo

RIMS Kokyuroku Bessatsu　42　137-152　2013/08
Publisher: Kyoto University
ISSN： 1881-6193
SMALL SOLUTIONS FOR NONLINEAR HEAT EQUATIONS, THE NAVIER-STOKES EQUATION, AND THE KELLER-SEGEL SYSTEM IN BESOV AND TRIEBEL-LIZORKIN SPACES

Tsukasa Iwabuchi, Makoto Nakamura

ADVANCES IN DIFFERENTIAL EQUATIONS　18　(7-8)　687-736　2013/07

ISSN： 1079-9389
GLOBAL SOLUTIONS FOR THE ROTATING NAVIER-STOKES EQUATIONS (Mathematical Analysis in Fluid and Gas Dynamics)

Iwabuchi Tsukasa, Takada Ryo

RIMS Kokyuroku　1830　34-41　2013/04
Publisher: Kyoto University
ISSN： 1880-2818
Time periodic solutions to the Navier-Stokes equations in the rotational framework

Tsukasa Iwabuchi, Ryo Takada

JOURNAL OF EVOLUTION EQUATIONS　12　(4)　985-1000　2012/12

DOI： 10.1007/s00028-012-0165-z 　

ISSN： 1424-3199
Global and almost global solutions for the Navier-Stokes equations in Besov spaces and Triebel-Lizorkin spaces

T. Iwabuchi, M. Nakamura

The 4th Japanese-German International Workshop on Mathematical Fluid Dynamics　p.8　2011/11
Global and almost global solutions for some nonlinear parabolic equations in Besov spaces and Triebel-Lizorkin spaces

T. Iwabuchi, M. Nakamura

The 4th MSJ-SI Nonlinear Dynamics in Partial Differential Equations　212-213　2011/09
Global well-posedness for Keller-Segel system in Besov type spaces

T. Iwabuchi

Journal of Mathematical Analaysis and Applications　379　(2)　930-948　2011/07

DOI： 10.1016/j.jmaa.2011.02.010 　
Global well-posedness for Keller-Segel system in Besov type spaces

Tsukasa Iwabuchi

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　379　(2)　930-948　2011/07

DOI： 10.1016/j.jmaa.2011.02.010 　

ISSN： 0022-247X
Well-posedness and ill-posedness for some nonlinear parabolic equations

T. Iwabuchi

The 3st GCOE International Symposium　2011/02
Existence of solution for Navier-Stokes equations in modulation spaces

T. Iwabuchi

RIMS Kokyuroku Bessatsu　B18　29-43　2010/06
Navier-Stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices

Tsukasa Iwabuchi

JOURNAL OF DIFFERENTIAL EQUATIONS　248　(8)　1972-2002　2010/04

DOI： 10.1016/j.jde.2009.08.013 　

ISSN： 0022-0396
Well-posedness for Navier-Stokes equations in modulation spaces with negative derivative indices

T. Iwabuchi

The 2st GCOE International Symposium　2010/02
Existence of solution for Navier-Stokes equations in modulation spaces

T. Iwabuchi

Some problems for Partial Differential Equations　2009/10
Well-posedness for Navier-Stokes equations in modulation spaces

T. Iwabuchi

The 1st GCOE International Symposium　2009/03
Well-posedness for nonlinear heat equations and Navier-Stokes equations in modulation spaces

T. Iwabuchi

The Euro-Japanese Workshop on Blow-up　2008/09

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Presentations 124

Sharp well-posedness and ill-posedness of the stationary quasi-geostrophic equation

Mikihiro Fujii, Tsukasa Iwabuchi

日本数学会　2025/09
分数冪ラプラシアンを有する表面準地衡方程式の解の一意性

Taiki Okazaki, Tsukasa Iwabuchi

日本数学会　2025/09
有界領域上における分数階微分に対するライプニッツ則について

Motofumi Aoki, Tsukasa Iwabuchi

日本数学会　2025/03
On the uniqueness for the two-dimensional surface quasi-geostrophic equation Invited

Tsukasa Iwabuchi

Fluids and Maximal Regularity　2024/09
Dyadic decomposition for the Dirichlet Laplacian applied to the SQG equation Invited

Tsukasa Iwabuchi

Analysis of PDEs in Fluid　2024/03
Dyadic decomposition for the Dirichlet Laplacian applied to the surface quasi-geostrophic equation Invited

Tsukasa Iwabuchi

応用解析研究会　2024/01
Dyadic decomposition of the spectrum for the Dirichlet Laplacian applied to the critical surface quasi-geostrophic equation Invited

Tsukasa Iwabuchi

East Asian Workshop on Partial Differential Equations from Kinetics and Continuum Mechanics in Tokyo　2023/11
Dyadic decomposition of the spectrum for the Dirichlet Laplacian applied to the critical surface quasi-geostrophic equation Invited

Tsukasa Iwabuchi

Critical phenomena in Nonlinear Partial Differential Equations, Harmonic analysis, and Functional inequalities　2023/11
A localized maximum principle and its application to the critical SQG on bounded domain Invited

Tsukasa Iwabuchi

ICIAM 2023　2023/08
On the ill-posedness for the full system of the compressible Navier-Stokes equation

Motofumi Aoki, Tsukasa Iwabuchi

日本数学会　2023/03
Optimality of the decay estimate of solutions to the linearised curl-free compressible Navier-Stokes equations

Dáithí Ó hAodha, Tsukasa Iwabuchi

日本数学会　2023/03
A localized maximum principle and its application to the critical SQG on bounded domain Invited

Tsukasa Iwabuchi

The 40th Kyushu Symposium on Partial Differential Equations　2023/02
A localized maximum principle and an application to the critical SQG on bounded domain Invited

Tsukasa Iwabuchi

International Workshop on Multiphase Flows: Analysis, Modelling and Numerics　2022/12
A localized maximum principle and its application to the critical SQG on bounded domain Invited

Tsukasa Iwabuchi

第１８３回神楽坂解析セミナー　2022/11
A sufficient condition for the energy conservation law of compressible Navier-Stokes equations

Motofumi Aoki, Tsukasa Iwabuchi

日本数学会　2022/09
On the energy conservation law for the full system of compressible Navier–Stokes equations

Motofumi Aoki, Tsukasa Iwabuchi

日本数学会　2022/03
表面準地衡方程式の解の最適な減衰評価

Dáithí Ó hAodha, Tsukasa Iwabuchi

日本数学会　2022/03
A spectral localization applied to the critical surface quasi-geostrophic equation on a ball

Tsukasa Iwabuchi

日本数学会　2022/03
Ill-posedness for compressible Navier-Stokes equations in two space dimensions Invited

Tsukasa Iwabuchi

京都大学NLPDEセミナー　2021/11
Ill-posedness for two dimensional compressible Navier–Stokes equations with scaling critical regularity

Tsukasa Iwabuchi

日本数学会　2021/09
Some bilinear estimates for functions with the Dirichlet boundary condition and an application to SQG Invited

Tsukasa Iwabuchi

RIMS Workshop on Mathematical Analysis in Fluid and Gas Dynamics　2021/07
臨界型 Burgers 方程式に対する解析性と長時間挙動について

Tsukasa Iwabuchi

応用数理解析セミナー　2021/04
Burgers equation with fractional dissipation Invited

Tsukasa Iwabuchi

若手による流体力学の基礎方程式研究集会　2021/03
Analyticity and large time behavior for the Burgers equation with the critical dissipation Invited

Tsukasa Iwabuchi

Quasi-linear PDEs in fluids　2021/02
Self-Similar solutions for compressible Navier-Stokes equations Invited

Tsukasa Iwabuchi

International Workshop on Multi-Phase Flows: Analysis, Modelling and Numerics　2020/12
Discontinuity of data-to-solution map for 2D compressible Navier-Stokes equations Invited

Tsukasa Iwabuchi

Vorticity, Rotation and Symmetry (V) – Global Results and Nonlocal Phenomena　2020/10
Analyticity and large time behavior for the Burgers equation with the critical dissipation

Tsukasa Iwabuchi

日本数学会　2020/09
Self-similar solutions for compressible Navier-Stokes equations Invited

Tsukasa Iwabuchi

第16回非線形の諸問題　2020/09
Self-similar solutions for compressible Navier-Stokes equations Invited

Tsukasa Iwabuchi

京都大学NLPDEセミナー　2020/06/14
DirichletおよびNeumann Laplacianに付随するSobolev空間における積の評価式

Tsukasa Iwabuchi

日本数学会　2020/03
Forward self-similar solutions for compressible Navier-Stokes equations

2020/03
Self-similar solutions for compressible Navier-Stokes equations Invited

Tsukasa Iwabuchi

Critical exponent and nonlinear evolution equations 2020　2020/02
Several properties of Besov spaces with Dirichlet boundary condition Invited

International Research Training Group 1529 Mathematical Fluid Dynamics, Harmonic Analysis and Nonlinear Partial Differential Equations　2019/01
The semigroup generated by the Dirichlet Laplacian of fractional order

Tsukasa Iwabuchi

AMS Sectional Meeting Program, Spring Central and Western Joint Sectional Meeting　2019/03
The semigroup generated by the Dirichlet Laplacian of fractional order

Tsukasa Iwabuchi

日本数学会　2018/09
分数冪のディリクレラプラシアンで生成される半群について Invited

Tsukasa Iwabuchi

南大阪応用数学セミナー　2018/07/21
Analyticity and Large Time Behavior of Solutions for the Burgers Equation with the Critical Dissipation Invited

Tsukasa Iwabuchi

The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications AIMS　2018/07
Besov spaces on open sets with the Dirichlet boundary condition and their application to the fractional Laplacian Invited

Tsukasa Iwabuchi

International Research Training Group 1529 Mathematical Fluid Dynamics　2018/05
Besov spaces on open sets with the Dirichlet boundary condition and their application to the fractional Laplacian Invited

Tsukasa Iwabuchi

京都大学NLPDEセミナー　2018/04/13
Analyticity and large time behavior of solutions for the Burgers equations with the critical dissipation International-presentation

Tsukasa Iwabuchi

Peking-Yamagata-Tohoku Universities joint workshop for Harmonic Analysis and PDE　2018/03/24
Analyticity and large time behavior of solutions for the Burgers equations with the critical dissipation International-presentation

Tsukasa Iwabuchi

FUKUSHIMA-TOHOKU-UOW PDE WORKSHOP　2018/03/01
圧縮性 Navier--Stokes 方程式に対する不適切性について Invited

Tsukasa Iwabuchi

日本数学会　2018/03
Dirichlet Laplacian で生成されるBesov空間

T. Iwabuchi, T. Matsuyama, K. Taniguchi

日本数学会　2018/03
領域上のBesov空間における双線形評価式

T. Iwabuchi, T. Matsuyama, K. Taniguchi

日本数学会　2018/03
Schr\"odinger 作用素によって生成される Besov 空間

T. Iwabuchi, T. Matsuyama, K. Taniguchi

日本数学会　2018/03
Besov spaces generated by the Dirichlet Laplacian and their properties

Tsukasa Iwabuchi

松山解析セミナー 2018　2018/02/03
Besov spaces on open sets with the Dirichlet boundary condition and an application to the fractional Laplacian International-presentation

Tsukasa Iwabuchi

Hyperbolic Partial Differential Equations and Related Topics　2018/01/27
Ill-posedness for the compressible Navier-Stokes equations under the barotropic condition International-presentation

Tsukasa Iwabuchi

The 15th Japanese-German International Workshop on Mathematical Fluid Dynamics　2018/01/12
一般領域上の超関数と関数空間論について

Tsukasa Iwabuchi

東北大学大学院理学研究科数学専攻談話会　2017/12/28
Dirichlet 境界条件付きの Besov 空間について

Tsukasa Iwabuchi

第 15 回浜松偏微分方程式研究集会　2017/12/23
Remark on the function spaces generated by the Dirichlet Laplacian and the Neumann Laplacian in one dimension International-presentation

Tsukasa Iwabuchi

Recent Topics on Partial Differential Equations　2017/11/19
Solvability and regularity for the Burgers equation with the critical dissipation

Tsukasa Iwabuchi

2017/10/27
Ill-posedness for the compressible Navier-Stokes Equations International-presentation

Tsukasa Iwabuchi

Analysis Seminar　2017/04/27
On the ill-posedness for some parabolic equations in the Besov spaces International-presentation

Tsukasa Iwabuchi

The 18th Northeastern Symposium on Mathematical Analysis　2017/02/21
Large time behavior of solutions for the Burgers equation with critical dissipation International-presentation

International Research Training Group 1529 seminar　2017/02/09
$L^1$ boundedness of spectral multipliers for the Dirichlet Laplacian on open sets International-presentation

International Research Training Group 1529 seminar　2016/12/07
Besov spaces generated by the Dirichlet Laplacian International-presentation

The 13th Japanese-German International Workshop on Mathematical Fluid Dynamics　2016/11/30
Besov spaces defined via the spectral theorem for the Dirichlet Laplacian International-presentation

The 14th Linear and Nonlinear Waves　2016/11/02
Besov spaces generated by the Dirichlet Laplacian International-presentation

Recent Topics on Dispersive Equations　2016/08/30
Besov spaces defined via the spectral theorem for the Dirichlet Laplacian

Ito Workshop on PDE　2016/08/22
開集合上の超関数と Besov 空間論

大阪市立大学数学研究所談話会　2016/07/20
Besov spaces defined via the spectral theorem for the Dirichlet Laplacian International-presentation

The 7th Pacific RIM Conference on Mathematics 2016　2016/06/27
Dirichlet Laplacian を用いて定義されるBesov空間

第 23 回応用解析研究会シンポジウム　2016/03
Besov spaces defined via the spectral theorem for the Dirichlet Laplacian International-presentation

The 8th Nagoya Workshop on Differential Equations　2016/02
On the large time behavior of small solutions for the critical Burgers equation International-presentation

3rd Chile-Japan Workshop on Nonlinear PDEs　2015/12
ポテンシャルで摂動されたBesov空間について

調和解析セミナー　2015/12
シュレディンガー作用素の関数に対する $L^p$-有界性とその応用

第 9 回実解析と函数解析による偏微分方程式論研究集会　2015/12
Schr\"odinger 作用素の関数の $L^p$-有界性について

谷口晃一, 松山登喜夫

日本数学会　2015/09
2次の非線形Sch\"odinger方程式系に対する非適切性について

瓜屋航太, 小川卓克

日本数学会　2015/09
臨界型Burgers方程式の時間大域解に対する漸近挙動

OCU Monday Seminar　2015/07
臨界型Burgers方程式の時間大域解に対する漸近挙動について

大阪大学微分方程式セミナー　2015/05
臨界型Burgers方程式の時間大域解に対する漸近挙動

京都大学NLPDEセミナー　2015/05
臨界型Burgers方程式の時間大域解と漸近挙動について

大阪市大・大阪府大合同「南大阪応用数学セミナー」　2015/04
臨界型Burgers方程式の時間大域解と漸近挙動

大阪市立大学数学研究所談話会　2015/04
On the large time behavior of solutions for the critical Burgers equations in the Besov spaces International-presentation

The 7th OCAMI-TIMS-Kobe-Waseda Joint International Workshop on Differential Geometry, Geometric Analysis and Mathematical Physics　2015/03
On the blow up criteria for the Navier-Stokes equations in Besov spaces

第 22 回応用解析研究会シンポジウム　2015/03
一般領域におけるBesov空間とその性質

三大学偏微分方程式セミナー　2015/02
On the blow up criteria of the Navier-Stokes equation in the Besov spaces

数理物理に現れる偏微分方程式研究会　2015/01
Global solutions for the Burgers equation in the Besov spaces and the large time behavior

日本数学会 / 学習院大学　2014
On the global solutions and the large time behavior for the critical Burgers equation in the Besov spaces

Conference on Partial Differential Equations 2014 / Monastery of Novacella　2014
On the ill-posedness for the drift-diffusion system in the homogeneous Besov spaces

Harmonic Analysis and Nonlinear Partial Differential Equations / 京都大学　2014
On the large time behavior of solutions for the critical Burgers equation

Seminar on Nonlinear Analysis at O-okayama / 東京工業大学　2014
Ill-posedness for the nonlinear Schr\"odinger equations in low space dimensions

Critical Exponents and Nonlinear Evolution Equation / 東京理科大学　2014
On the large time behavior of solutions for the critical Burgers equation

第21回応用解析研究会シンポジウム / 箱根の森おかだ　2014
臨界型Burgers方程式の時間大域解と漸近挙動について

第125回神楽坂解析セミナー / 東京理科大学　2014
On the ill-posedness for the nonlinear Schr\"odinger equations in low space dimensions

Asymptotic Analysisfor Nonlinear Dispersive and Wave Equations / 大阪大学　2014
Ill-posedness for the drift diffusion system in the homogeneous Besov spaces

Nonlinear Dispersive Equations and Harmonic Analysis / 京都大学　2014
臨界型Burgers方程式の時間大域解と漸近挙動について

九州関数方程式セミナー / 九州大学　2014
臨界型Burgers方程式の時間大域解と漸近挙動について

信州大学偏微分方程式研究集会 / 信州大学　2014
空間1次元と2次元における非線形シュレディンガー方程式の非適切性について

埼玉大学数理解析セミナー / 埼玉大学　2013
低次元における非線形シュレディンガー方程式の非適切性について

早稲田大学非線形解析勉強会 / 早稲田大学　2013
Global solutions for the Navier-Stokes equations in the rotational framework

The 8th Japanese-German International Workshop on Mathematical Fluid Dynamics / 早稲田大学　2013
Ill-posedness for the nonlinear Schr\"odinger equations in low space dimensions

Linear and Nonlinear Wave No. 11 / 滋賀県立県民交流センター　2013
コリオリ項付きのNavier-Stokes方程式に対する時間大域解について

若手による流体力学の基礎方程式研究集会　2013
コリオリ項付きNavier-Stokes方程式の時間大域解について

Geophysical Fluid Dynamics / Oberwolfach　2013
コリオリ項付きNavier-Stokes 方程式の時間大域解

The 3nd International GCOE symposium on ``Weaving Science Web beyond Particle-Matter Hierarchy'' / 東北大学　2013
Global solutions for the Navier-Stokes equations in the rotational framework

Harmonic Analysis and PDEs on Manifolds / 中央大学　2013
移流拡散方程式の初期値問題に対する非適切性について

日本数学会 / 愛媛大学　2013
Ill-posednes for the Schr\"odinger equations in one and two space dimensions

9th International ISAAC Congress / Krakow　2013
Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type

日本数学会関数方程式分科会アブストラクト／日本数学会　2012
空間１次元における非線形シュレディンガー方程式の非適切性について

京都大学NLPDEセミナー / 京都大学　2012
空間１次元および２次元における非線形シュレディンガー方程式の非適切性について

第105回神楽坂解析セミナー/ 東京理科大学　2012
コリオリ項付きナヴィエ-ストークス方程式に対する時間大域解について

Vortex Theory Now, Frontiers Mathematical Physics / 大阪大学　2012
空間低次元における非線形シュレディンガー方程式の非適切性について

微分方程式の総合的研究 / 京都大学　2012
コリオリ項を持つナヴィエ-ストークス方程式の時間局所解について

三大学微分方程式セミナー / 中央大学　2012
空間１次元における非線形シュレディンガー方程式の非適切性について

幾何学的偏微分方程式に対する保存則と正則性特異性の研究 / 京都大学　2012
1次元と2次元における非線形シュレディンガー方程式の非適切性について

数理と現象 : Mathematics and Phenomena in Miyazaki 2012 / 宮崎大学　2012
空間１次元における非線形シュレディンガー方程式の非適切性について

応用解析研究会 / 早稲田大学　2012
コリオリ項付きのナヴィエ-ストークス方程式の時間大域解について

流体と気体の数学解析 / 京都大学　2012
コリオリ項付きナヴィエ-ストークス方程式に対する時間大域解について

Parabolic and Navier-Stokes equations / ポーランド　2012
空間1次元と2次元における2次の非線形項を有する非線形シュレディンガー方程式の非適切性について

Nonlinear Dispersive Equations and Fluid Mechanics -Well-posedness and Smoothing Effect- / 東北大学　2012
Global and almost global solutions for some nonlinear parabolic equations in Besov spaces and Triebel-Lizorkin spaces

日本数学会関数方程式分科会アブストラクト／日本数学会　2011
Global and almost global solutions for some nonlinear parabolic equations in Besov spaces and Triebel-Lizorkin spaces

岐阜大学における微分方程式セミナーアブストラクト／岐阜大学　2011
斉次Besov空間における放物-楕円型Keller-Segel方程式の解の適切性と非適切性について

学習院大学スペクトル理論セミナーアブストラクト／学習院大学　2010
斉次Besov空間を用いたKeller-Segel系の時間大域解について

日本数学会関数方程式分科会アブストラクト／日本数学会　2010
斉次Besov空間を用いた放物-放物型Keller-Segel系の時間大域解について

日本数学会関数方程式分科会アブストラクト／日本数学会　2010
Modulation空間におけるNavier-Stokes方程式の解の存在定理について

調和解析セミナーアブストラクト／日本大学　2010
斉次Besov空間における放物-楕円型Keller-Segel方程式の解の適切性と非適切性について

神楽坂解析セミナーアブストラクト／東京理科大学　2010
斉次Besov空間における放物-楕円型Keller-Segel方程式の時間大域解について

発展方程式若手セミナー報告集／発展方程式若手セミナー　2010
Modulation空間におけるNavier-Stokes方程式の解の存在定理について

発展方程式若手セミナー報告集／発展方程式若手セミナー　2009
Modulation空間におけるNavier-Stokes方程式の解の存在定理について

日本数学会関数方程式分科会アブストラクト／日本数学会　2009
非線形熱方程式とNavier-Stokes方程式に対するModulation空間を用いた解の存在定理について

日本数学会関数方程式分科会アブストラクト／日本数学会　2008
非線形熱方程式とNavier-Stokes方程式に対するModulation空間を用いた解の存在定理について

発展方程式若手セミナー報告集／発展方程式若手セミナー　2008
非線形シュレディンガー方程式の解の存在定理について

発展方程式若手セミナー報告集／発展方程式若手セミナー　2007

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Research Projects 7

Creation of advanced method in mathematical analysis on nonlinear mathematical models of critical type

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (S)

Institution: Tohoku University

2019/06/26 - 2024/03/31
Invention and explorer for undiscovered structure and principle in the mathematical analysis for the relation between fluid dynamics and combustion.

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Challenging Research (Pioneering)

Institution: Tohoku University

2020/04/01 - 2023/03/31
Well-posedness for the nonlinear partial differential equations in critical spaces

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Young Scientists (A)

Institution: Tohoku University

2017/04/01 - 2021/03/31
Unravel higher order critical structures to solutions of nonlinear dispersive and dissipative partial differential equations

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (A)

Institution: Tohoku University

2019/04/01 - 2020/03/31
Elucidations on unexplored regions of problems related to the criticality of nonlinear dissipative and dispersive structures in mathematical models

Ogawa Takayoshi, Shimizu Senjo, Kurokiba Masaki, Iwabuchi Tsukasa, Wakui Hiroshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (S)

Institution: Tohoku University

2013/05/31 - 2018/03/31

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We extract a dispersive and dissipative effect from the typical example in the nonlinear dispersive equations such as the nonlinear Schroedinger equation and nonlinear dissipative equations such as the Navier-Stokes system or the drift diffusion system and research the critical problems that arose from a balanced situation between the stabilize effects from dispersive and dissipative and the instability caused from nonlinear interaction. In particular, we establish the maximal regularity for the nonlinear dissipative system and applied for the critical problems and singular limit problems in Keller-Segel system or ill-posedness problem of mathematical fluid mechanics.
Well-posedness and ill-posedness for the nonlinear partial differential equations

IWABUCHI Tsukasa

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Young Scientists (B)

2013/04/01 - 2017/03/31

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This work is concerned with revealing and understanding the optimal initial condition for some nonlinear partial differential equations such as Navier-Stokes equations and Schrodinger equations. We studied the Navier-Stokes equations in the spaces of functions which have the bounded mean oscillation property, and also gave some initial condition for the equations with the Coriolis force. As to Schrodinger equations, we proved ill-posedness with quadratic non-linearity. It is also proved for the Burgers equation with the critical dissipation that small global solution tends to the Poisson kernel.
非線形偏微分方程式の初期値問題の適切性と非適切性の研究 Competitive

2010 -

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