Details of the Researcher

PHOTO

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）

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

  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 32

  1. 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

  2. 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

  3. 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.

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

    More details Close

    <p lang="fr">&lt;p style='text-indent:20px;'&gt;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.&lt;/p&gt;</p>

  10. 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

  11. 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

  12. Self-similar solutions of the compressible Navier-Stokes equations Peer-reviewed

    P. Germain, T. Iwabuchi

    Arch. Ration. Mech. Anal.　240　(3)　1645-1673　2021

  13. 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

  14. Backward self-similar solutions for compressible Navier-Stokes equations Peer-reviewed

    P. Germain, T. Iwabuchi, T. Léger

    Nonlinearity　34　(2)　868-893　2021

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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 　

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  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

  12. 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 　

  13. 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

  14. Well-posedness and ill-posedness for some nonlinear parabolic equations

    T. Iwabuchi

    The 3st GCOE International Symposium　2011/02

  15. Existence of solution for Navier-Stokes equations in modulation spaces

    T. Iwabuchi

    RIMS Kokyuroku Bessatsu　B18　29-43　2010/06

  16. 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

  17. Well-posedness for Navier-Stokes equations in modulation spaces with negative derivative indices

    T. Iwabuchi

    The 2st GCOE International Symposium　2010/02

  18. Existence of solution for Navier-Stokes equations in modulation spaces

    T. Iwabuchi

    Some problems for Partial Differential Equations　2009/10

  19. Well-posedness for Navier-Stokes equations in modulation spaces

    T. Iwabuchi

    The 1st GCOE International Symposium　2009/03

  20. 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 85

  1. 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

  2. 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

  3. 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

  4. Dirichlet Laplacian で生成されるBesov空間

    T. Iwabuchi, T. Matsuyama, K. Taniguchi

    日本数学会　2018/03

  5. 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

  6. 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

  7. Besov spaces generated by the Dirichlet Laplacian and their properties

    Tsukasa Iwabuchi

    松山解析セミナー 2018　2018/02/03

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. Solvability and regularity for the Burgers equation with the critical dissipation

    Tsukasa Iwabuchi

    2017/10/27

  14. Ill-posedness for the compressible Navier-Stokes Equations International-presentation

    Tsukasa Iwabuchi

    Analysis Seminar　2017/04/27

  15. 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

  16. Large time behavior of solutions for the Burgers equation with critical dissipation International-presentation

    International Research Training Group 1529 seminar　2017/02/09

  17. $L^1$ boundedness of spectral multipliers for the Dirichlet Laplacian on open sets International-presentation

    International Research Training Group 1529 seminar　2016/12/07

  18. Besov spaces generated by the Dirichlet Laplacian International-presentation

    The 13th Japanese-German International Workshop on Mathematical Fluid Dynamics　2016/11/30

  19. Besov spaces defined via the spectral theorem for the Dirichlet Laplacian International-presentation

    The 14th Linear and Nonlinear Waves　2016/11/02

  20. Besov spaces generated by the Dirichlet Laplacian International-presentation

    Recent Topics on Dispersive Equations　2016/08/30

  21. Besov spaces defined via the spectral theorem for the Dirichlet Laplacian

    Ito Workshop on PDE　2016/08/22

  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

  23. Besov spaces defined via the spectral theorem for the Dirichlet Laplacian International-presentation

    The 7th Pacific RIM Conference on Mathematics 2016　2016/06/27

  24. 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

  25. Besov spaces defined via the spectral theorem for the Dirichlet Laplacian International-presentation

    The 8th Nagoya Workshop on Differential Equations　2016/02

  26. On the large time behavior of small solutions for the critical Burgers equation International-presentation

    3rd Chile-Japan Workshop on Nonlinear PDEs　2015/12

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. 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

  37. 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

  38. 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

  39. 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

  40. 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

  41. 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

  42. 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

  43. 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

  44. 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

  45. 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

  46. 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

  47. 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

  48. Ill-posedness for the drift diffusion system in the homogeneous Besov spaces

    Nonlinear Dispersive Equations and Harmonic Analysis / 京都大学　2014

  49. 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

  50. 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

  51. 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

  52. 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

  53. 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

  54. 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

  55. 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

  56. 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

  57. 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

  58. Global solutions for the Navier-Stokes equations in the rotational framework

    Harmonic Analysis and PDEs on Manifolds / 中央大学　2013

  59. 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

  60. Ill-posednes for the Schr\"odinger equations in one and two space dimensions

    9th International ISAAC Congress / Krakow　2013

  61. 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

  62. 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

  63. 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

  64. 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

  65. 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

  66. 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

  67. 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

  68. 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

  69. 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

  70. 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

  71. 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

  72. 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

  73. 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

  74. 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

  75. 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

  76. 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

  77. 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

  78. 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

  79. 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

  80. 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

  81. 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

  82. 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

  83. 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

  84. 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

  85. 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

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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.

  6. 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

    More details Close

    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.

  7. 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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