Vanishing viscosity and the accumulation of vorticity on the boundary

We say that the vanishing viscosity limit holds in the classical sense if the velocity for a solution to the Navier-Stokes equations converges in the energy norm uniformly in time to the velocity for a solution to the Euler equations. We prove, for a bounded domain in dimension 2 or higher, that the vanishing viscosity limit holds in the classical sense if and only if a vortex sheet forms on the boundary.

Keywords

Vanishing viscosity, incompressible fluid mechanics

2010 Mathematics Subject Classification

76B99, 76D05, 76D99

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Published 1 January 2008