Communications in Mathematical Sciences

Volume 6 (2008)

Number 4

Vanishing viscosity and the accumulation of vorticity on the boundary

Pages: 869 – 880

DOI: http://dx.doi.org/10.4310/CMS.2008.v6.n4.a4

Author

J. P. Kelliher

Abstract

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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