﻿ Inviscid limit of incompressible Navier-Stokes equations-同济大学数学科学学院

Inviscid limit of incompressible Navier-Stokes equations

2022年7月26日（星期二）15:00-16:00

2022年7月27日（星期三）15:00-16:00

2022年7月28日（星期四）15:00-16:00

2022年7月29日（星期五）15:00-16:00

Determining the behavior of viscous flows at small viscosity is one of the most fundamental problems in fluid mechanics. In this talk, we focus on the incompressible flow and study the vanishing viscosity limit of incompressible Navier-Stokes equations. It mainly involves the following contents:

（I）Inviscid limit without physical boundary.

For this case, the inviscid limit problem is easy for strong solution (conclude the convergence rate), but it’s difficult for weak solution (singular solution). We mainly study the inviscid limit for weak solution, including vortex patch and point vortices.

（II）Inviscid limit with physical boundary.

For this case, we first introduce the simple case--Navier-Slip boundary condition, then focus on the no-slip boundary condition. For the no-slip boundary, the boundary layer is strong and is determined by Prandtl equation. In this part, we mainly study the well-posedness of Prandtl equation and the inviscid limit for no-slip boundary.

（III）Inviscid limit for the steady Navier-Stokes equations in torus and disk.

In this part, we study the steady Navier-Stokes equations in torus with rotating boundary condition and mainly study the famous Prandtl-Batchlor theory.