Mathematical analysis of dispersion and anisotropy in rotating fluids

2014 Fiscal Year Final Research Report

• Project/Area Number: 25887005
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Mathematical analysis
• Research Institution: Tohoku University
• Principal Investigator: TAKADA RYO 東北大学, 理学(系)研究科(研究院), 助教 (50713236)
• Project Period (FY): 2013-08-30 – 2015-03-31
• Keywords: 偏微分方程式 / 流体力学 / 非圧縮性流体 / 回転流体 / Navier-Stokes 方程式 / Euler 方程式 / Coriolis 力 / 分散型評価

Outline of Final Research Achievements

This research project aims to analyze nonlinear partial differential equations describing the motion of incompressible rotating fluids mathematically. We established dispersive and space-time estimates for the linear propagator generated by the Coriolis force. As an application, we proved the long time existence of solutions to the initial value problem for the incompressible rotating Euler equations. It is expected that our results and techniques obtained in this research can be applied to the study of the rotating shallow water equations and the primitive equations.

Free Research Field

数物系科学