Vorticity measures and the inviscid limit

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.

arXiv comment14 pages

References in corpus (5)

• Mathematics and Turbulence: where do we stand?
• Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows
• Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit
• Remarks on high Reynolds numbers hydrodynamics and the inviscid limit
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Cited by in corpus (3)

• On the Euler+Prandtl expansion for the Navier-Stokes equations
• Inviscid damping and enhanced dissipation of the boundary layer for 2D Navier-Stokes linearized around Couette flow in a channel
• Singularity formation of vortex sheets in 2D Euler equations using the characteristic mapping method