The convergence of the solutions of the Navier-Stokes equations to that of the Euler equations
The full (nonlinear) Navier-Stokes equations in space dimension two is considered. Under physically reasonable assumptions it is proved that the solutions to the Navier-Stokes equations converge to the solutions of Euler equations on any finite interval of time. The assumptions on the solutions are either the boundedness at the wall accepted in turbulence theory, or a moderate growth condition for the tangential derivative of the tangential flow near the wall, physical relevance of which is discussed in the text. The flow in a channel of rectangular geometry is considered.
scientific article; zbMATH DE number 1107192