Vorticity measures and the inviscid limit

TL;DR

This paper investigates conditions on vorticity measures that guarantee the convergence of 2D Navier-Stokes solutions to Euler solutions as viscosity approaches zero, especially in the context of vortex sheets.

Contribution

It establishes sufficient conditions on vorticity measures away from boundaries that ensure inviscid limit convergence, aligning with vortex sheet solutions.

Findings

Identifies conditions on vorticity measures for inviscid limit convergence

Connects vortex sheet solutions with the inviscid limit behavior

Provides a framework for analyzing boundary effects in 2D flows

Abstract

We consider a sequence of Leray-Hopf weak solutions of the 2D Navier-Stokes equations on a bounded domain, in the vanishing viscosity limit. We provide sufficient conditions on the associated vorticity measures, away from the boundary, which ensure that as the viscosity vanishes the sequence converges to a weak solution of the Euler equations. These assumptions are consistent with vortex sheet solutions of the Euler equations.