The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

TL;DR

This paper reviews recent mathematical progress on the inviscid limit of Navier-Stokes equations, focusing on convergence to Euler solutions both with and without physical boundaries and the role of boundary layers.

Contribution

It provides a comprehensive review of recent advances in understanding the inviscid limit and boundary layer effects in fluid mechanics.

Findings

Progress in mathematical analysis of inviscid limit

Understanding boundary layer influence

Convergence results for Navier-Stokes to Euler

Abstract

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physical boundary is present and the effect of the boundary layer becomes significant. The aim of this article is to review recent progress on the mathematical analysis of this problem in each category.