Vanishing viscosity and the accumulation of vorticity on the boundary. (English) Zbl 1161.76012
Summary: We say that the vanishing viscosity limit holds in the classical sense if the velocity for a solution to Navier-Stokes equations converges in the energy norm uniformly in time to the velocity for a solution to 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.
MSC:
76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
76B03 | Existence, uniqueness, and regularity theory for incompressible inviscid fluids |
35Q30 | Navier-Stokes equations |
35Q35 | PDEs in connection with fluid mechanics |