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.
@article{1229619674,
author = {Kelliher, J. P.},
title = {Vanishing viscosity and the accumulation of vorticity on the boundary},
journal = {Commun. Math. Sci.},
volume = {6},
number = {1},
year = {2008},
pages = { 869-880},
language = {en},
url = {http://dml.mathdoc.fr/item/1229619674}
}
Kelliher, J. P. Vanishing viscosity and the accumulation of vorticity on the boundary. Commun. Math. Sci., Tome 6 (2008) no. 1, pp. 869-880. http://gdmltest.u-ga.fr/item/1229619674/