The inviscid limit for the $2d$ Navier-Stokes equations in bounded domains

TL;DR

This paper establishes the inviscid limit for 2D Navier-Stokes equations in bounded domains with boundary-analytic data, using a vorticity approach and linear semigroup analysis.

Contribution

It provides a direct proof of the inviscid limit in bounded domains with boundary-analytic data, combining vorticity formulation and semigroup techniques.

Findings

Proves inviscid limit for 2D Navier-Stokes in bounded domains.

Uses vorticity formulation with nonlocal boundary conditions.

Employs explicit semigroup of linear Stokes problem.

Abstract

We prove the inviscid limit for the incompressible Navier-Stokes equations for data that are analytic only near the boundary in a general two-dimensional bounded domain. Our proof is direct, using the vorticity formulation with a nonlocal boundary condition, the explicit semigroup of the linear Stokes problem near the flatten boundary, and the standard wellposedness theory of Navier-Stokes equations in Sobolev spaces away from the boundary.