(1) Department of Mathematics, Brown University, Box 1917, Providence, RI 02912, USA;(2) University of California, Riverside, 900 University Ave., Riverside, CA 92521, USA
Abstract:
We say that a solution of the Navier–Stokes equations converges in the vanishing viscosity limit to a solution of the Euler
equations if their velocities converge in the energy (L2) norm uniformly in time as the viscosity ν vanishes. We show that a necessary and sufficient condition for the vanishing viscosity limit to hold in a disk is that the
space–time energy density of the solution to the Navier–Stokes equations in a boundary layer of width proportional to ν vanish with ν, and that one need only consider spatial variations whose frequencies in the radial or tangential direction lie in a band
centered around 1/ν.
The author was supported in part by NSF grant DMS-0705586 during the period of this work.