古典場の理論における微分型相互作用の数学解析

• Project/Area Number: 19H00644
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Medium-sized Section 12:Analysis, applied mathematics, and related fields
• Research Institution: Waseda University
• Principal Investigator: 小澤 徹 早稲田大学, 理工学術院, 教授 (70204196)
• Co-Investigator(Kenkyū-buntansha): 田中 和永 早稲田大学, 理工学術院, 教授 (20188288) ; 町原 秀二 埼玉大学, 理工学研究科, 教授 (20346373) ; BEZ NEAL 埼玉大学, 理工学研究科, 教授 (30729843)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Project Status: Granted (Fiscal Year 2023)
• Budget Amount: ¥43,680,000 (Direct Cost: ¥33,600,000、Indirect Cost: ¥10,080,000); Fiscal Year 2023: ¥10,010,000 (Direct Cost: ¥7,700,000、Indirect Cost: ¥2,310,000); Fiscal Year 2022: ¥9,620,000 (Direct Cost: ¥7,400,000、Indirect Cost: ¥2,220,000); Fiscal Year 2021: ¥9,620,000 (Direct Cost: ¥7,400,000、Indirect Cost: ¥2,220,000); Fiscal Year 2020: ¥8,710,000 (Direct Cost: ¥6,700,000、Indirect Cost: ¥2,010,000); Fiscal Year 2019: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
• Keywords: 調和解析 / 漸近解析

Outline of Research at the Start

微分型シュレディンガー方程式をはじめとする微分型相互作用を持つ古典場模型の非線型偏微分方程式は、ピカール逐次近似の枠組において、必然的に微分の損失を伴うため、その回避を巡って方程式に応じた個別の方法論が提案されているが、未だに本質的な理解に至っていない。本研究の目的は、近年の微分型シュレディンガー方程式の初期値問題の時間大域的存在を保障する新しい閾値の変分解析的理解を足掛かりとして、微分型相互作用の大域的構造を(a)漸近解析(b)調和解析(c)変分解析の三つの方法論に基づいて明らかにする事である。

Outline of Annual Research Achievements

半線型構造の枠組における微分型相互作用の研究から、半線型構造から準線型構造への展開研究に重点を置いて研究を進めた。
具体的には、半線型分散方程式を対象とした研究においては、分散構造の研究を行い、準線型波動方程式を対象とした研究においては、ハミルトン構造の研究を行った。特に、円環（トーラス）上の微分的非線型シュレディンガー方程式の強解の存在と一意性に対しては、従来より未解決の問題を肯定的に解決した。また、対数型相互作用をもつ非線型シュレディンガー方程式に対しては、従来のさまざまな結果を統一的に説明する理論体系を構築するとともに未解決な問題の多くを解決した。ここで用いられた近似方程式の解法は汎用性が高く、対数型相互作用をもつ非線型シュレディンガー方程式のみならず、対数型相互作用をもつ非線型熱方程式や複素ギンツブルグ方程式にも適用可能性が見出されたので、その一般論を整備中である。ハミルトン構造の研究に関しては、強解の大域的存在を保障する「修正エネルギーの方法」の汎用化・一般化を進めるとともに、その変分構造が時間に対する第二次変分公式に起因することを明らかにした。また、可積分方程式の第二次エネルギーと修正エネルギーを比較検討することにより、その重要な項とそうでない項の分類を行い、修正エネルギーの本質を明らかにした。
研究班ごとの実施状況は、(a)漸近解析の方法論による分散構造の研究、(b)調和解析の方法論による分散構造の研究、(c)変分解析の方法論によるハミルトン構造の研究をそれぞれ進めた。

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

研究計画は予定通り順調に進んでいる。現在までの研究で思いがけない着想が幾つか得られており、今後の進展に繋がる事が期待される。

Strategy for Future Research Activity

今迄に得られた成果を論文としてまとめるとともに、国内外の研究者が参加する研究集会を利用して一層の活発な研究討論を図る計画である。

Research Products

• [Int'l Joint Research] 南京林業大学/China Jiliang University/Zhejiang University,(中国)
• [Int'l Joint Research] Jeonbuk National University/Ewha Womans University(韓国)
• [Int'l Joint Research] 南京林業大学/Beijing Normal University/Fujian Normal University(中国)
• [Int'l Joint Research] Jeonbuk National University/Chunbuk National University/Ewha Womans University(韓国)
• [Int'l Joint Research] Universita degli Studi di Bari Aldo Moro(イタリア)
• [Int'l Joint Research] University of Birmingham(英国)
• [Int'l Joint Research] Nazarbayev University(カザフスタン)
• [Int'l Joint Research] Seoul National University(韓国)
• [Int'l Joint Research] Beijing Normal University/Fujian Normal University(中国)
• [Int'l Joint Research] Utah State University(米国)
• [Int'l Joint Research] Nazarbayev University(カザフスタン)
• [Int'l Joint Research] ピサ大学(イタリア)
• [Int'l Joint Research] Nanjing Forestry University(中国)
• [Journal Article] Blow-up solutions for a class of divergence Schr\"{o}dinger equations with intercritical inhomogeneous nonlinearity (2023)
  • Author(s): J. Zhai, T. Ozawa, B. Zheng
  • Journal Title: Journal of Mathematical Physics Volume: 64 Issue: 1
  • DOI: 10.1063/5.0098298
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Charge conjugation approach to scattering for the Hartree type Dirac equations with chirality (2023)
  • Author(s): Y. Cho, S. Hong, T. Ozawa
  • Journal Title: Journal of Mathematical Physics Volume: 64 Issue: 2
  • DOI: 10.1063/5.0118132
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Revisiting the Rellich inequality (2023)
  • Author(s): N. Bez, S. Machihara, T. Ozawa
  • Journal Title: Mathematische Zeitschrift Volume: 303 Issue: 2 Pages: 49-49
  • DOI: 10.1007/s00209-022-03203-4
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Schrodinger-improved Boussinesq system in two space dimensions (2022)
  • Author(s): Ozawa Tohru、Tomioka Kenta
  • Journal Title: Journal of Evolution Equations Volume: 22 Issue: 2
  • DOI: 10.1007/s00028-022-00793-8
  • Peer Reviewed / Open Access
• [Journal Article] Magnetohydrodynamics approximation of the compressible full magneto-micropolar system (2022)
  • Author(s): J. Fan, T. Ozawa
  • Journal Title: AIMS Mathematics Volume: 7 Issue: 9 Pages: 16037-16053
  • DOI: 10.3934/math.2022878
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Remarks on the Navier-Stokes equations in space dimension $n \geq 3$ (2022)
  • Author(s): J. Fan, T. Ozawa
  • Journal Title: Proceedings of the American Mathematical Society, Series B Volume: 9 Issue: 30 Pages: 317-324
  • DOI: 10.1090/bproc/135
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Well-posedness for the Chern-Simons-Schr\"{o}dinger equations (2022)
  • Author(s): J. Fan, T. Ozawa
  • Journal Title: AIMS Mathematics Volume: 7 Issue: 9 Pages: 17349-17356
  • DOI: 10.3934/math.2022955
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities (2022)
  • Author(s): Cingolani Silvia、Gallo Marco、Tanaka Kazunaga
  • Journal Title: Calculus of Variations and Partial Differential Equations Volume: 61 Issue: 2 Pages: 68-68
  • DOI: 10.1007/s00526-021-02182-4
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Nonlinear elliptic equations of sublinearity: qualitative behavior of solutions (2022)
  • Author(s): Ikoma Norihisa、Tanaka Kazunaga、Wang Zhi-Qiang、Zhang Chengxiang
  • Journal Title: Indiana University Mathematics Journal Volume: 71 Issue: 5 Pages: 2001-2043
  • DOI: 10.1512/iumj.2022.71.9168
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation (2022)
  • Author(s): Inui Takahisa、Machihara Shuji
  • Journal Title: Journal of Hyperbolic Differential Equations Volume: 19 Issue: 03 Pages: 407-437
  • DOI: 10.1142/s0219891622500126
  • Peer Reviewed
• [Journal Article] Small data scattering of 2d Hartree type Dirac equations (2022)
  • Author(s): Cho Yonggeun、Lee Kiyeon、Ozawa Tohru
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: 506 Issue: 1 Pages: 125549-125549
  • DOI: 10.1016/j.jmaa.2021.125549
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Zakharov system in two space dimensions (2022)
  • Author(s): Ozawa Tohru、Tomioka Kenta
  • Journal Title: Nonlinear Analysis Volume: 214 Pages: 112532-112532
  • DOI: 10.1016/j.na.2021.112532
  • Peer Reviewed / Open Access
• [Journal Article] Regularity Criteria for a Ginzburg-Landau-Navier-Stokes System (2021)
  • Author(s): J. Fan, T. Ozawa
  • Journal Title: Funkcialaj Ekvacioj Volume: 64 Issue: 3 Pages: 349-360
  • DOI: 10.1619/fesi.64.349
  • NAID: 130008131858
  • ISSN: 0532-8721
  • Year and Date: 2021-12-15
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Small Data Scattering of Hartree Type Fractional Schrödinger Equations in a Scaling Critical Space (2021)
  • Author(s): Cho Yonggeun、Ozawa Tohru、Yang Changhun
  • Journal Title: Funkcialaj Ekvacioj Volume: 64 Issue: 1 Pages: 1-15
  • DOI: 10.1619/fesi.64.1
  • NAID: 130008023886
  • ISSN: 0532-8721
  • Year and Date: 2021-04-15
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A note on 2D Navier-Stokes equations (2021)
  • Author(s): Fan Jishan、Ozawa Tohru
  • Journal Title: Partial Differential Equations and Applications Volume: 2 Issue: 6 Pages: 73-73
  • DOI: 10.1007/s42985-021-00129-0
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Uniform Regularity for a Compressible Gross-Pitaevskii-Navier-Stokes System (2021)
  • Author(s): J. Fan, T. Ozawa
  • Journal Title: Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 346) Volume: 346 Pages: 95-102
  • DOI: 10.1007/978-981-33-4822-6_3
  • ISBN: 9789813348219, 9789813348226
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A note on bilinear estimates in the homogeneous Triebel-Lizorkin spaces (2021)
  • Author(s): J. Fan, T. Ozawa
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B88 Pages: 147-150
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] On fractional Schroedinger equations with Hartree type nonlinearities (2021)
  • Author(s): Cingolani Silvia、Tanaka Kazunaga
  • Journal Title: Mathematics in Engineering Volume: 4 Issue: 6 Pages: 1-33
  • DOI: 10.3934/mine.2022056
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Erratum: Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation (2021 Nonlinearity 34 4017) (2021)
  • Author(s): Cingolani S、Gallo M、Tanaka K
  • Journal Title: Nonlinearity Volume: 34 Issue: 10 Pages: C3-C3
  • DOI: 10.1088/1361-6544/ac166f
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation (2021)
  • Author(s): Cingolani S、Gallo M、Tanaka K
  • Journal Title: Nonlinearity Volume: 34 Issue: 6 Pages: 4017-4056
  • DOI: 10.1088/1361-6544/ac0166
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass (2021)
  • Author(s): Cingolani Silvia、Tanaka Kazunaga
  • Journal Title: Geometric properties for parabolic and elliptic PDEs, Springer INdAM Ser. 47 Volume: 47 Pages: 23-41
  • DOI: 10.1007/978-3-030-73363-6_2
  • ISBN: 9783030733629, 9783030733636
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Deformation Argument under PSP Condition and Applications (2021)
  • Author(s): S. Cingolani, K. Tanaka
  • Journal Title: Analysis in Theory and Applications Volume: 37 Issue: 2 Pages: 191-208
  • DOI: 10.4208/ata.2021.pr80.03
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Semi-classical states for logarithmic Schr?dinger equations (2021)
  • Author(s): Ikoma Norihisa、Tanaka Kazunaga、Wang Zhi-Qiang、Zhang Chengxiang
  • Journal Title: Nonlinearity Volume: 34 Issue: 4 Pages: 1900-1942
  • DOI: 10.1088/1361-6544/abd52a
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Higher order transversality in harmonic analysis (2021)
  • Author(s): J. Bennett, N. Bez
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B88 Pages: 75-103
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Poincare inequalities with exact missing terms on homogeneous groups (2021)
  • Author(s): OZAWA Tohru、SURAGAN Durvudkhan
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 73 Issue: 2 Pages: 497-503
  • DOI: 10.2969/jmsj/83738373
  • NAID: 130008029572
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates (2021)
  • Author(s): Bez Neal, Lee Sanghyuk, Nakamura Shohei
  • Journal Title: Forum of Mathematics, Sigma Volume: 9 Pages: 1-52
  • DOI: 10.1017/fms.2020.64
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Existence and uniqueness of classical paths under quadratic potentials (2020)
  • Author(s): Narita Kazuki, Ozawa Tohru
  • Journal Title: Calculus of Variations and Partial Differential Equations Volume: 59 Issue: 4 Pages: 128-128
  • DOI: 10.1007/s00526-020-01791-9
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Global solutions to the Maxwell-Navier-Stokes system in a bounded domain in 2D (2020)
  • Author(s): Fan Jishan, Ozawa Tohru
  • Journal Title: Zeitschrift f\"ur angewandte Mathematik und Physik Volume: 71 Issue: 4 Pages: 136-136
  • DOI: 10.1007/s00033-020-01364-y
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Sharp remainder of the Poincar\'e inequality (2020)
  • Author(s): Ozawa Tohru, Suragan Durvudkhan
  • Journal Title: Proceedings of the American Mathematical Society Volume: 148 Issue: 10 Pages: 4235-4239
  • DOI: 10.1090/proc/15119
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Multidimensional inverse Cauchy problems for evolution equations (2020)
  • Author(s): Karazym Mukhtar, Ozawa Tohru, Suragan Durvudkhan
  • Journal Title: Inverse Problems in Science and Engineering Volume: 28 Issue: 11 Pages: 1582-1590
  • DOI: 10.1080/17415977.2020.1739034
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Well-posedness of a 2D time-dependent Ginzburg-Landau superconductivity model (2020)
  • Author(s): Fan Jishan, Ozawa Tohru
  • Journal Title: Nonlinear Analysis and Differential Equations Volume: 8 Issue: 1 Pages: 89-97
  • DOI: 10.12988/nade.2020.91126
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Blowup solutions for the nonlinear Schr\"odinger equation with complex coefficient (2020)
  • Author(s): S. Kawakami, S. Machihara
  • Journal Title: Differential Integral Equations Volume: 33
  • Peer Reviewed
• [Journal Article] Sharp ill-posedness of the Dirac-Klein-Gordon system in one dimension (2020)
  • Author(s): Machihara Shuji, Okamoto Mamoru
  • Journal Title: Nonlinear Analysis Volume: 192 Pages: 111687-111687
  • DOI: 10.1016/j.na.2019.111687
  • Peer Reviewed / Open Access
• [Journal Article] Maximal estimates for the Schr\"odinger equation with orthonormal initial data (2020)
  • Author(s): Bez Neal, Lee Sanghyuk, Nakamura Shohei
  • Journal Title: Selecta Mathematica Volume: 26 Issue: 4 Pages: 26-52
  • DOI: 10.1007/s00029-020-00582-6
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Cauchy problem and vanishing dispersion limit for Schr\"odinger-improved Boussinesq equations (2020)
  • Author(s): Fan Jishan、Ozawa Tohru
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: 485 Issue: 2 Pages: 123857-123857
  • DOI: 10.1016/j.jmaa.2020.123857
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Hardy type inequalities with spherical derivatives (2020)
  • Author(s): Bez Neal、 Machihara Shuji、 Ozawa Tohru
  • Journal Title: SN Partial Differ. Equ. Appl. Volume: 1, Issue 1 Issue: 1
  • DOI: 10.1007/s42985-019-0001-1
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases (2020)
  • Author(s): Fujiwara Kazumasa、Georgiev Vladimir、Ozawa Tohru
  • Journal Title: J. Math. Pures Appl. Volume: 136 Pages: 239-256
  • DOI: 10.1016/j.matpur.2019.10.003
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A blow-up criterion for the modified Navier-Stokes-Fourier equations (2020)
  • Author(s): Fan Jishan、Ozawa Tohru
  • Journal Title: Journal of Mathematical Fluid Mechanics Volume: 22 Issue: 2
  • DOI: 10.1007/s00021-019-0477-7
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A note on bilinear estimates in the Sobolev spaces (2019)
  • Author(s): Fan Jishan、Ozawa Tohru
  • Journal Title: International Journal of Mathematical Analysis Volume: 13 Issue: 12 Pages: 551-554
  • DOI: 10.12988/ijma.2019.91064
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Semi-classical states for the nonlinear Choquard equations: existence, multiplicity and concentration at a potential well (2019)
  • Author(s): Cingolani Silvia、Tanaka Kazunaga
  • Journal Title: Rev. Mat. Iberoam. Volume: 35 Issue: 6 Pages: 1885-1924
  • DOI: 10.4171/rmi/1105
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A note on deformation argument for $L^2$ normalized solutions of nonlinear Schr\"odinger equations and systems (2019)
  • Author(s): Ikoma Norihisa、Tanaka Kazunaga
  • Journal Title: Adv. Differential Equations Volume: 24 Pages: 609-646
  • Peer Reviewed
• [Presentation] Semi-classical states for nonlinear Choquard equations: Concentration around local maxima or saddle points in degenerate setting (2023)
  • Author(s): K. Tanaka
  • Organizer: “Workshop on Variational Methods and Functional Inequalities” (RIMS 訪問滞在型研究計画)
  • Int'l Joint Research / Invited
• [Presentation] Existence of normalized solutions for L2-critical NLS (2023)
  • Author(s): K. Tanaka
  • Organizer: 第１７回非線形偏 微分方程式と変分問題
• [Presentation] Stability of the log-Sobolev and hypercontractivity inequalities (2023)
  • Author(s): N. Bez
  • Organizer: Variational Methods and Functional Inequalities
  • Int'l Joint Research / Invited
• [Presentation] Boundary Strichartz estimates for orthonormal systems (2023)
  • Author(s): N. Bez
  • Organizer: The 40th Kyushu Symposium on Partial Differential Equations
  • Int'l Joint Research / Invited
• [Presentation] 非線型分散方程式に関する修正エネルギー法 (2022)
  • Author(s): T. Ozawa
  • Organizer: 日本数学会２０２２年度秋季総合分科会 企画特別講演
  • Invited
• [Presentation] 2次元領域に於けるザハロフ系 (2022)
  • Author(s): T. Ozawa
  • Organizer: Dispersive and wave equations
  • Invited
• [Presentation] 修正エネルギー法について (2022)
  • Author(s): T. Ozawa
  • Organizer: 黒木場正城教授 追悼研究集会「非線型偏微分方程式と走化性」
  • Invited
• [Presentation] Method of Modified Energy (2022)
  • Author(s): T. Ozawa
  • Organizer: International Workshop on Multi-Phase Flows: Analysis, Modelling and Numerics
  • Int'l Joint Research / Invited
• [Presentation] Semi-classical states for nonlinear Choquard equations: Concentration around local maxima or saddle points in degenerate setting (2022)
  • Author(s): K. Tanaka
  • Organizer: Qualitative and quantitative aspects of nonlinear PDEs
  • Int'l Joint Research / Invited
• [Presentation] Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities (2022)
  • Author(s): K. Tanaka
  • Organizer: International Conference on Nonlinear Analysis and Nonlinear Partial Differential Equations
  • Int'l Joint Research / Invited
• [Presentation] L2直交性から眺める Rellich の不等式 (2022)
  • Author(s): S. Machihara
  • Organizer: 解析学とその周辺
  • Invited
• [Presentation] 等式から眺める Rellich の不等式 (2022)
  • Author(s): S. Machihara
  • Organizer: 九州関数方程式セミナー
  • Invited
• [Presentation] プラズマ現象の数学的理解 (2022)
  • Author(s): T. Ozawa
  • Organizer: 日本物理学会第77回年次大会 プラズマサイエンスの新展開 シンポジウム講演
  • Invited
• [Presentation] Deformation Argument under PSP Condition and Applications (2021)
  • Author(s): K. Tanaka
  • Organizer: Thematic Session: Variational Equations and Applications to Differential Equations, 33o Col´oquio Brasileiro de Matem´atica, IMPA
  • Int'l Joint Research / Invited
• [Presentation] Spherical harmonics and Hardy's inequalities (2021)
  • Author(s): S. Machihara
  • Organizer: 2021 RIMS共同研究(公開型)「量子場の数理とその周辺」
  • Int'l Joint Research / Invited
• [Presentation] Pointwise convergence for the Schroedinger equation with orthonormal initial data (2021)
  • Author(s): N. Bez
  • Organizer: 8th European Congress of Mathematics minisymposium “Harmonic Analysis and Partial Differential Equations”
  • Int'l Joint Research / Invited
• [Presentation] Dispersive estimates for the wave equation (2021)
  • Author(s): N. Bez
  • Organizer: Harmonic Analysis and Wave Phenomena
  • Int'l Joint Research / Invited
• [Presentation] The nonlinear Brascamp-Lieb inequality (2021)
  • Author(s): N. Bez
  • Organizer: MSJ-KMS Joint Meeting
  • Int'l Joint Research / Invited
• [Presentation] Brascamp-Liebの不等式の安定性 (2022年度日本数学会賞春季賞受賞講演) (2021)
  • Author(s): N. Bez
  • Organizer: 日本数学会2022年度年会
  • Invited
• [Presentation] 球面微分とハーディの不等式 (2021)
  • Author(s): S. Machihara
  • Organizer: Workshop on Analysis in Kagurazaka 2021
  • Invited
• [Presentation] On the Poincar\'e and Related Inequalities (2020)
  • Author(s): T. Ozawa
  • Organizer: International Workshop on Multiphase Flows: Analysis, Modelling and Numerics
  • Int'l Joint Research / Invited
• [Presentation] 非線形楕円型方程式の解の存在問題 --- Pohozaev の等式を巡って --- (2020)
  • Author(s): 田中和永
  • Organizer: 微分方程式の総合的研究，日本数学会関数方程式分科会
  • Int'l Joint Research / Invited
• [Presentation] ポワンカレの不等式・温故知新 (2020)
  • Author(s): Ozawa Tohru
  • Organizer: 大阪大学 微分方程式セミナー
  • Invited
• [Presentation] Spherical Harmonics and Hardy’s equality (2020)
  • Author(s): Machihara Shuji
  • Organizer: Recent Progress on Dispersive and Wave Equations
  • Int'l Joint Research / Invited
• [Presentation] A new deformation result for singular perturbation problems (2020)
  • Author(s): Tanaka Kazunaga
  • Organizer: 第 14 回非線形偏微分方程式と変分問題
• [Presentation] Self-similar solutions to the derivative nonlinear Schr\"odinger equation (2019)
  • Author(s): Ozawa Tohru
  • Organizer: International Conference “Actual Problems of Analysis, Differential Equations and Algebra”(National academy of sciences of the Republic of Kazakhstan)
  • Int'l Joint Research / Invited
• [Presentation] Singular perturbation problems for nonlinear Choquard equations (2019)
  • Author(s): Tanaka Kazunaga
  • Organizer: 東京工業大学理学部数学教室談話会
  • Invited
• [Book] Birkh\"auser (2023)
  • Author(s): T. Ozawa (Ed.)
  • Total Pages: 394
  • Publisher: Collected Papers in Honor of Yoshihiro Shibata
• [Book] Viscosity solutions - Dedicated to Hitoshi Ishii on the award of the 1st Kodaira Kunihiko Prize (2022)
  • Author(s): K. Ishige, S. Koike, T. Ozawa, and S. Shimizu (Eds.)
  • Publisher: SN Partial Differential Equations and Applications
• [Book] Mathematical Fluid Mechanics and Related Topics: In Honor of Professor Hideo Kozono's 60th Birthday (2022)
  • Author(s): K. Ishige, T. Ozawa, S. Shimizu, and Y. Taniuchi (Eds.)
  • Publisher: SN Partial Differential Equations and Applications
• [Book] Proceedings of 46th Sapporo Symposium on Partial Differential Equations (2021)
  • Author(s): S. Ei, Y. Giga, N. Hamamuki, S. Jimbo, H. Kubo, H. Kuroda, Y. Liu, T. Ozawa, T. Sakajo, and K. Tsutaya (Eds.)
  • Total Pages: 108
  • Publisher: Hokkaido University Technical Report Series in Mathematics
• [Book] Proceedings of 45th Sapporo Symposium on Partial Differential Equations (2020)
  • Author(s): S. Ei, Y. Giga, N. Hamamuki, S. Jimbo, H. Kubo, H. Kuroda, H. Kuroda, T. Ozawa, T. Sakajo, and K. Tsutaya (Eds.),
  • Total Pages: 98
  • Publisher: Hokkaido University Technical Report Series in Mathematics
• [Book] Trends in Mathematics (2020)
  • Author(s): V. Georgiev, T. Ozawa, M. Ruzhansky, and J. Wirth (Eds.),
  • Total Pages: 317
  • Publisher: Birkh\"auser
• [Book] The Role of Metrics in the Theory of Partial Differential Equations (2020)
  • Author(s): Y. Giga, N. Hamamuki, H. Kubo, H. Kuroda, and T. Ozawa (Eds.)
  • Total Pages: 543
  • Publisher: Mathematical Society of Japan
• [Book] New Tools for Nonlinear PDEs and Application, Trends in Mathematics (2019)
  • Author(s): M. D'Abbicco, M. R. Ebert, V. Georgiev, and T. Ozawa (Eds.)
  • Total Pages: 390
  • Publisher: Birkh\"auser
  • ISBN: 9783030109363
• [Book] Asymptotic analysis of nonlinear dispersive and wave equations (2019)
  • Author(s): K. Kato, T. Ogawa, and T. Ozawa (Eds.)
  • Total Pages: 419
  • Publisher: Mathematical Society of Japan
  • ISBN: 9784864970815
• [Remarks] 早稲田大学 理工学術院 先進理工学部 応用物理学科 小澤徹研究室
  • URL: https://www.ozawa.phys.waseda.ac.jp/index2.html
• [Remarks] 早稲田大学理工学術院先進理工学部応用物理学科 小澤 徹 研究室
  • URL: http://www.ozawa.phys.waseda.ac.jp/index2.html
• [Remarks] 早稲田大学理工学術院 先進理工学部応用物理学科 小澤 徹研究室
  • URL: http://www.ozawa.phys.waseda.ac.jp/index2.html