Singular Limit for Rotating Compressible Fluids with Centrifugal Force in a Finite Cylinder

Abstract

In this paper, we consider a rotating compressible Navier–Stokes system in a finite cylinder, by incorporating the effect of centrifugal force. The Mach number and Froude number admit the same scale. By using the relative entropy method, we prove that the scaled problem approaches the static profile as the Mach and Reynolds numbers tend to zero and infinity respectively, with well-prepared initial data. In particular, the property of radial symmetry resulting from the centrifugal force is crucial in the whole analysis.