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Vorticity Measures and the Inviscid Limit

2019; Springer Science+Business Media; Volume: 234; Issue: 2 Linguagem: Inglês

10.1007/s00205-019-01398-1

1432-0673

Peter Constantin, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes, Vlad Vicol,

Geometric Analysis and Curvature Flows

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.