2018 Fiscal Year Final Research Report
Mathematical Analysis of Critical Interactions in Classical Fields
| Project/Area Number |
26247014
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Waseda University |
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Principal Investigator |
OZAWA Tohru 早稲田大学, 理工学術院, 教授 (70204196)
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| Co-Investigator(Kenkyū-buntansha) |
和田出 秀光 金沢大学, 機械工学系, 准教授 (00466525)
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)
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| Research Collaborator |
KATAYAMA Soichiro
SUNAGAWA Hideaki
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Keywords | 調和解析 / 漸近解析 / 非線形解析 |
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| Outline of Final Research Achievements |
Regarding the critical interactions in the theory of classical fields, we have studied equations of nonrelativistic fields and of semirelativistic fields and related inequalities appearing in the analysis of those equations. As for the nonlinear Shr\"odinger equations, we proved blow-up of solutions in non-gauge invariant setting.
Moreover, we have improved the Br\'ezis-Gallou\"et argument by renormalizing higher order energy to cover higher order nonlinearities in the global Cauchy problem for nonrelativistic and semirelativistic equations.
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| Free Research Field |
数学解析
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| Academic Significance and Societal Importance of the Research Achievements |
場の古典論に現れる方程式は、ド・ブロイの視点により、物質を波と捉えてモデル化した方程式である。従って、場の方程式の解の存在を示すことは、物質が現象として意味を持っていることの証明を与えることと同値となり、研究成果の学術的意義・社会的意義を示すこととなる。
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