Multiple Scales and Singular Limits for Compressible Rotating Fluids with General Initial Data

Abstract

We study the singular limit of a rotating compressible fluid described by a scaled barotropic Navier-Stokes system, where the Rossby number = ϵ, the Mach number = ϵ m , the Reynolds number = ϵ−α, and the Froude number = ϵ n are proportional to a small parameter ϵ → 0. The inviscid planar Euler system is identified as the limit problem. The proof is based on the application of the method of relative entropies and careful analysis of oscillatory integrals describing the propagation of Rossby-acoustic waves.