Diffusion wave property of the solutions to the system of the viscous fluid flow

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400175
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Osaka University
• Principal Investigator: Takayuki Kobayashi 大阪大学, 基礎工学研究科, 教授 (50272133)
• Co-Investigator(Kenkyū-buntansha): KAJIKIYA RYUJI 佐賀大学, 大学院工学系研究科, 教授 (10183261)
• Co-Investigator(Renkei-kenkyūsha): KAGEI YOSHIYUKI 九州大学, 大学院数理学研究院, 教授 (80243913) ; MISAWA MASASHI 熊本大学, 大学院自然科学研究科, 教授 (40242672) ; KUBO TAKAYUKI 筑波大学, 数理物質科学研究科, 講師 (90424811)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 圧縮性流体 / Navier-Stokes 方程式 / Stokes 方程式 / 消散型波動方程式 / 非線形波動方程式 / 線形粘性弾性体方程式

Outline of Final Research Achievements

We consider the initial boundary value problems for incompressible Navier-Stokes equations in half space and perturbed half space. We proved the time decay estimates for the solutions in weighted Lp space. We also consider the semilinear heat equations and dissipative wave equations in two dimension exterior domains. We showed the L2 boundedness with respect to the space and time valuables of the solutions for initial data in the Hardy space.

Free Research Field

偏微分方程式論