Mathematical analysis to nonstationary Navier-Stokes equations in a domain with piecewise smooth boundaries

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540156
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hirosaki University
• Principal Investigator: ITOH SHIGEHARU 弘前大学, 教育学部, 教授 (40193487)
• Co-Investigator(Kenkyū-buntansha): OKABE Takahiro 弘前大学, 教育学部, 講師 (00626872)
• Co-Investigator(Renkei-kenkyūsha): TANI Atusi 慶応義塾大学, 名誉教授 (90118969) ; TANAKA Naoto 福岡大学, 理学部, 教授 (00247222)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: ナヴィエ・ストークス方程式 / ストークス方程式 / 角がある領域 / エネルギー減衰

Outline of Final Research Achievements

The free surface problem to the Navier-Stokes equations that the movement of the liquid in a glass or the waterdrop on the table become the concrete examples was studied. In a plain sector, the series solution of the linearized equation which converges uniformly was constructed. Thus, it is possible that the solutions are estimated precisely in the Hoelder space or the Sobolev-Slobodekii space.
Moreover, we consider the Navier-Stokes equations in the half-spaces and derived the lower bound of the rate of the energy decay of the flow. Especially, we succeeded to characterize the profile of the initial data which causes such a lower bound for the flow.

Free Research Field

数物系科学