Mathematical research on mechanical problems of incompressible fluid

2022 Fiscal Year Final Research Report

• Project/Area Number: 18H01137
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Gakushuin University
• Principal Investigator: Okamoto Hisashi 学習院大学, 理学部, 教授 (40143359)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: Navier-Stokes equations

Outline of Final Research Achievements

The Kolmogorov problems for the two-dimensional Navier-Stokes equations was studied and a kind of universal patterns for large vortices were confirmed by the numerical experiments. Water-waves on two vortical layers were computed numerically, and many highly nontrivial solutions of many stagnation points were discovered.New method of computing the blow-up time for nonlinear parabolic equations were proposed.

Free Research Field

mathematics

Academic Significance and Societal Importance of the Research Achievements

特異摂動の問題に極めて不思議な解が存在することを数値実験で確かめた。それを保証する数学的な理論も部分的に提出された。しかし、完全な解決には程遠い。これらは次の世代への問題と言うことができる。特にプラントル・バチェラー理論の一般化には大きな魅力を感じる。