Vorticity Measures and the Inviscid Limit

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. The main assumptions are local interior uniform bounds on the L 1 -norm of vorticity and the local uniform convergence to zero of the total variation of vorticity measure on balls, in the limit of vanishing ball radii.