Communications in Mathematical Sciences
Volume 6 (2008)
Vanishing viscosity and the accumulation of vorticity on the boundary
Pages: 869 – 880
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.
Vanishing viscosity; incompressible fluid mechanics
2010 Mathematics Subject Classification
76B99, 76D05, 76D99