Mamoru Okamoto

Last Updated :2025/04/25

Affiliations, Positions
Hiroshima University, Professor
E-mail
mokamotohiroshima-u.ac.jp
Other Contact Details
1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima, Japan
TEL : (+81)82-424-7338 FAX : (+81)
Self-introduction
I am studying nonlinear dispersive equations with probabilistic effects.

Basic Information

Major Professional Backgrounds

  • 2025/04, Hiroshima University, Graduate School of Advanced Science and Engineering, Professor
  • 2020/04, 2025/03, Osaka University, Graduate School of Science Department of Mathematics, Associate Professor
  • 2014/04, 2020/03, Shinshu University,, Faculty of Engineering, Division of Mathematics and Physics, Assistant Professor
  • 2013/04, 2014/03, Kyoto University, Research Fellow of the Japan Society for the Promotion of Science (DC2)

Educational Backgrounds

  • Kyoto University, Graduate School of Science, Division of Mathematics and Mathematical Sciences, 2011/04, 2014/03
  • Kyoto University, Graduate School of Science, Division of Mathematics and Mathematical Sciences, 2009/04, 2011/03
  • Saitama University, Faculty of Science, Department of Mathematics, 2005/04, 2009/03

Academic Degrees

  • Doctor of Science, Kyoto University

Research Activities

Academic Papers

  1. Norm inflation for a higher-order nonlinear Schr\"odinger equation with a derivative on the circle, Partial Differential Equations and Applications, 6(2), 20250312
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  2. ★, Stochastic Quantization of the $\Phi^3_3$-Model, Memoirs of the European Mathematical Society, 20250205
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  3. Well-Posedness for a System of Nonlinear Schr\"odinger Equations with Derivative Nonlinearity via the Energy Method, Trends in Mathematics, 147-164, 20250130
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  4. ★, Focusing $\Phi^4_3$-model with a Hartree-type Nonlinearity, Memoirs of the American Mathematical Society, 304(1529), 20241210
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  5. A remark on randomization of a general function of negative regularity, Proceedings of the American Mathematical Society, Series B, 11(47), 538-554, 20241018
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  6. Uniqueness and non-uniqueness of the Gaussian free field evolution under the two-dimensional Wick ordered cubic wave equation, Annales de l'Institut Henri Poincar\'e, Probabilit\'es et Statistiques, 60(3), 20240801
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  7. On the local linearization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing, Proceedings of the American Mathematical Society, Series B, 11(34), 378-389, 20240711
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  8. Norm inflation for the viscous nonlinear wave equation, Nonlinear Differential Equations and Applications, 31(4), 202407
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  9. Sharp well-posedness for the Cauchy problem of the two dimensional quadratic nonlinear Schr\"odinger equation with angular regularity, Journal of Differential Equations, 395, 181-222, 20240625
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  10. A REMARK ON THE WELL-POSEDNESS FOR A SYSTEM OF QUADRATIC DERIVATIVE NONLINEAR SCHR\"ODINGER EQUATIONS, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 202206
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  11. Long-time behavior of solutions to a fourth-order nonlinear Schr\"odinger equation with critical nonlinearity, JOURNAL OF EVOLUTION EQUATIONS, 202108
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  12. Well-posedness for a system of quadratic derivative nonlinear Schr\"odinger equations in almost critical spaces, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 499(2), 202107
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  13. Comparing the stochastic nonlinear wave and heat equations: a case study, Electronic Journal of Probability, 26(none), 20210101
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  14. Random data Cauchy problem for the quadratic nonlinear Schr\"odinger equation without gauge invariance, Advanced Studies in Pure Mathematics, 85, 337-347, 202012
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  15. A remark on norm inflation for nonlinear wave equations, Dynamics of Partial Differential Equations, 17(4), 361-381, 202011
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  16. A remark on triviality for the two-dimensional stochastic nonlinear wave equation, STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 130(9), 5838-5864, 202009
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  17. Well-posedness for KdV-type equations with quadratic nonlinearity, JOURNAL OF EVOLUTION EQUATIONS, 20(3), 811-835, 202009
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  18. Well-Posedness for a System of Quadratic Derivative Nonlinear Schr\"odinger Equations with Radial Initial Data, ANNALES HENRI POINCARE, 21(8), 2611-2636, 202008
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  19. Scattering for the one-dimensional Klein–Gordon equation with exponential nonlinearity, Journal of Hyperbolic Differential Equations, 17(02), 295-354, 202006
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  20. Sharp ill-posedness of the Dirac-Klein-Gordon system in one dimension, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 192, 202003
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  21. On the stochastic nonlinear Schr\"odinger equations at critical regularities, STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 202001
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  22. FINAL STATE PROBLEM FOR THE NONLOCAL NONLINEAR SCHR\"ODINGER EQUATION WITH DISSIPATIVE NONLINEARITY, DIFFERENTIAL EQUATIONS & APPLICATIONS, 11(4), 481-494, 201911
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  23. ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A HIGHER-ORDER KDV-TYPE EQUATION WITH CRITICAL NONLINEARITY, EVOLUTION EQUATIONS AND CONTROL THEORY, 8(3), 567-601, 201909
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  24. L^p-L^q ESTIMATES FOR THE DAMPED WAVE EQUATION AND THE CRITICAL EXPONENT FOR THE NONLINEAR PROBLEM WITH SLOWLY DECAYING DATA, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 18(4), 1967-2008, 201907
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  25. ON THE PROBABILISTIC WELL-POSEDNESS OF THE NONLINEAR SCHR\"ODINGER EQUATIONS WITH NON-ALGEBRAIC NONLINEARITIES, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 39(6), 3479-3520, 201906
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  26. Remarks on the probabilistic well-posedness for quadratic nonlinear Schr\"odinger equations, RIMS Kôkyûroku Bessatsu, B74, 47-64, 201904
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  27. LONG-TIME BEHAVIOR OF SOLUTIONS TO THE FIFTH-ORDER MODIFIED KDV-TYPE EQUATION, ADVANCES IN DIFFERENTIAL EQUATIONS, 23(9-10), 751-792, 201809
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  28. On the cubic Dirac equation with potential and the Lochak-Majorana condition, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 456(2), 1203-1237, 201712
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  29. Well-posedness for the dimension-reduced Chern-Simons-Dirac system, JOURNAL OF EVOLUTION EQUATIONS, 17(3), 1031-1048, 201709
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  30. Large time asymptotics of solutions to the short-pulse equation, NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 24(4), -, 201708
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  31. Norm inflation for the generalized Boussinesq and Kawahara equations, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 157, 44-61, 201707
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  32. RANDOM DATA CAUCHY PROBLEM FOR THE NONLINEAR SCHR\"ODINGER EQUATION WITH DERIVATIVE NONLINEARITY, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 36(12), 6943-6974, 201612
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  33. Well-posedness for a quadratic derivative nonlinear Schr\"odinger system at the critical regularity, JOURNAL OF FUNCTIONAL ANALYSIS, 271(4), 747-798, 201608
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  34. BLOWUP AND ILL-POSEDNESS RESULTS FOR A DIRAC EQUATION WITHOUT GAUGE INVARIANCE, EVOLUTION EQUATIONS AND CONTROL THEORY, 5(2), 225-234, 201606
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  35. WELL-POSEDNESS AND ILL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE GENERALIZED THIRRING MODEL, DIFFERENTIAL AND INTEGRAL EQUATIONS, 29(5-6), 401-420, 201605
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  36. WELL-POSEDNESS AND SCATTERING FOR FOURTH ORDER NONLINEAR SCHR\"ODINGER TYPE EQUATIONS AT THE SCALING CRITICAL REGULARITY, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 15(3), 831-851, 201605
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  37. ★, Sharp Well-Posedness and Ill-Posedness for the Chern-Simons-Dirac System in One Dimension, INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 1640-1694, 2016
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  38. Remarks on ill-posedness for the Dirac-Klein-Gordon system, DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 13(3), 179-190, 2016
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  39. Ill-posedness of the Cauchy problem for the Chem-Simons-Dirac system in one dimension, JOURNAL OF DIFFERENTIAL EQUATIONS, 258(4), 1356-1394, 201502
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  40. Well-posedness of the Cauchy problem for the Maxwell-Dirac system in one space dimension, NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS, 64, 497-505, 2015
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  41. WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE CHERN-SIMONS-DIRAC SYSTEM IN TWO DIMENSIONS, JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 10(4), 735-771, 201312
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  42. WELL-POSEDNESS AND ILL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE MAXWELL DIRAC SYSTEM IN 1+1 SPACE TIME DIMENSIONS, ADVANCES IN DIFFERENTIAL EQUATIONS, 18(1-2), 179-199, 201301
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Invited Lecture, Oral Presentation, Poster Presentation

  1. Well- and ill-posedness of the Cauchy problem for a system of periodic quadratic derivative NLS, Mamoru Okamoto, Asia-Pacific International Conference on Dispersive Equations, 2024/10/31, With Invitation
  2. On the stochastic quantization of the $\Phi^3_3$-model, Mamoru Okamoto, Harmonic and Stochastic Analysis of Dispersive PDEs, 2024/06/07, With Invitation
  3. On the solutions to the two-dimensional Wick ordered nonlinear Klein-Gordon equation, Mamoru Okamoto, The 41th Kyushu Symposium on Partial Differential Equations, 2024/01/24, With Invitation
  4. Uniqueness of the Gaussian free field evolution under the Wick ordered nonlinear Klein-Gordon equation, Mamoru Okamoto, New trends in nonlinear dispersive equations, 2024/01/18, With Invitation
  5. Stochastic quantization of the $\Phi^3_3$-model, Mamoru Okamoto, Nonlinear and Random Waves, 2022/10/03, With Invitation
  6. On the $\Phi^3_3$ measure, Mamoru Okamoto, the 42nd conference on Stochastic Processes and their Applications, 2022/06/30, With Invitation
  7. Stochastic quantization of the $\Phi^3_3$-model, Mamoru Okamoto, Rigorous statistical mechanics and related topics, 2021/11/17, With Invitation
  8. Almost sure global well-posedness for the focusing nonlinear wave equation with a Hartree-type nonlinearity, Mamoru Okamoto, Oberseminar Analysis, 2021/01/08, With Invitation, Universitat Bielefeld
  9. On the critical exponent for the damped nonlinear wave equation with slowly decaying data, Mamoru Okamoto, Analysis Seminar, 2019/07/11, With Invitation
  10. On the damped nonlinear wave equation with slowly decaying data, Mamoru Okamoto, UK Network on Hyperbolic Equations and Related Topics, 2019/05/16, With Invitation
  11. On the energy critical nonlinear Schrodinger equations with randomized initial data, Mamoru Okamoto, Stochastic partial differential equations and related topics, 2018/07/26, With Invitation
  12. Random data Cauchy problem for the energy-critical nonlinear Schrodinger equations, Mamoru Okamoto, The 11th Mathematical Society of Japan Seasonal Institute, 2018/07/03, With Invitation
  13. Random data Cauchy problem for the energy-critical nonlinear Schrodinger equations, Mamoru Okamoto, Harmonic Analysis and Nonlinear Partial Differential Equations, 2018/06/26, With Invitation
  14. Random data Cauchy problem for the energy critical nonlinear Schrodinger equations, Mamoru Okamoto, Nonlinear Dispersive Equations in Kumamoto, 2018/01/21, With Invitation
  15. Asymptotic behavior of solutions to the short-pulse equation, Mamoru Okamoto, Analysis Seminar, 2017/09/25, With Invitation
  16. Asymptotic behavior of solutions to the short-pulse equation, Mamoru Okamoto, The 5th East Asian Conference in Harmonic Analysis and Applications, 2017/06/10, With Invitation
  17. Sharp well-posedness and ill-posedness for the Chern-Simons-Dirac system in one dimension, Mamoru Okamoto, Harmonic Analysis and Partial Differential Equations, 2015/07/27, Without Invitation
  18. Sharp well-posedness for the Chern-Simons-Dirac system in one dimension, Mamoru Okamoto, The 39th Sapporo Symposium on Partial Differential Equations, 2014/08/25, With Invitation
  19. On the Cauchy problem of the generalized Thirring equations, Mamoru Okamoto, Seminar in Mathematics, 2014/03/27, With Invitation
  20. Well-posedness and ill-posedness for a system for the Chern-Simons-Dirac system in one dimension, Mamoru Okamoto, Critical exponents and nonlinear evolution equations, 2014/02/10, With Invitation
  21. Ill-posedness for the Chern-Simons-Dirac system in one dimension, Mamoru Okamoto, Nonlinear Dispersive Equations and Harmonic Analysis, 2014/01/14, With Invitation
  22. Ill-posedness of the Cauchy problem for the Chern-Simons-Dirac system in one dimension, Mamoru Okamoto, Seminar in nonlinear PDE center, 2013/11/13, With Invitation
  23. Well-posedness for the Chern-Simons-Dirac system in two dimensions, Mamoru Okamoto, Nonlinear Dispersive Equations and Related Topics, 2013/07/03, With Invitation
  24. Well-posedness for the Chern-Simons-Dirac system, Mamoru Okamoto, Kyoto RIMS-SNU workshop, 2013/02/18, Without Invitation
  25. Well-posedness for the Chern-Simons-Dirac system in two dimensions, Mamoru Okamoto, Doctoral Forum of Mathematics between Fudan and Kyoto Universities, 2012/12/08, Without Invitation
  26. Well-posedness and ill-posedness of the Cauchy problem for the Maxwell-Dirac system in 1+1 space time dimensions, Mamoru Okamoto, Nonlinear Wave and Dispersive Equations, 2012/03/08, With Invitation
  27. Well-posedness of the Maxwell-Dirac system in 1+1 space time dimensions, Mamoru Okamoto, Doctoral Forum of Mathematics between Fudan and Kyoto Universities, 2011/10/31, Without Invitation
  28. Well-posedness of the Maxwell-Dirac system in 1+1 space time dimensions, Mamoru Okamoto, the 4th MSJ-SI, 2011/09/20, Without Invitation
  29. Well-posedness of the Maxwell-Dirac system in 1+1 space time dimensions, Mamoru Okamoto, Mathematical Analysis in Fluid and Gas Dynamics, 2011/07/08, With Invitation
  30. Well-posedness of the Maxwell-Dirac system in 1+1 space time dimensions, Mamoru Okamoto, Doctorial Forum Fudan-Kyoto, 2011/03/14, Without Invitation

Social Activities

History as Committee Members

  1. Editor, 2025/04, Hiroshima Mathematical Journal
  2. Organizer, 2025/04, Hiroshima Mathematical Analysis Seminar