Mathematical Analysis for local and nonlocal structures in viscous flows

2015 Fiscal Year Final Research Report

• Project/Area Number: 25800079
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Tohoku University
• Principal Investigator: MAEKAWA Yasunori 東北大学, 理学(系)研究科(研究院), 准教授 (70507954)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: Navier-Stokes方程式 / 流体力学 / 渦度場 / 境界層 / 解の漸近挙動

Outline of Final Research Achievements

This research project is aimed to achieve the understanding of mathematical structure of solutions to the Navier-Stokes equations for viscous inompressible flows, which are fundamental equations in fluid dynamics. This project has revealed various important structures of vorticity fields for the Navier-Stokes flows: the stability of boundary layer when the initial vorticty is located away from the boundary, the asymptotic behavior of solutions to the Navier-Stokes equations in two-dimensional exterior domains, the asymptotic stability of some stationary solutions to the exterior flows around a rotating disk, regularity criterion for the three-dimensional Navier-Stokes equations in the half space under the condition of voricity direction and type I blow-up, the vorticity boundary condition n the half plane and its applications.

Free Research Field

偏微分方程式論