Vanishing viscosity limit for incompressible flow inside a rotating circle

In this article we consider circularly symmetric incompressible viscous flow in a disk. The boundary condition is no-slip with respect to a 4 prescribed time-dependent rotation of the boundary about the center of the disk. We prove that, if the prescribed angular velocity of the boundary 5 has finite total variation, then the Navier–Stokes solutions converge strongly in L2 to the corresponding stationary solution of the Euler equations 6 when viscosity vanishes. Our approach is based on a semigroup treatment of the symmetry-reduced scalar equation. 7 c © 2008 Published by Elsevier B.V. 8