Multiple scales and singular limits for compressible rotating fluids with general initial data

TL;DR

This paper investigates the behavior of rotating compressible fluids under multiple scaling limits, showing convergence to the Euler system and analyzing wave propagation using entropy methods.

Contribution

It introduces a rigorous analysis of the singular limits for rotating compressible fluids with general initial data, combining entropy methods and wave analysis.

Findings

Convergence to the Euler system in the singular limit

Identification of Rossby-acoustic wave propagation effects

Application of relative entropy method to complex fluid limits

Abstract

We study the singular limit of a rotating compressible fluid described by a scaled barotropic Navier-Stokes system, where the Rossby number, the Mach number and the Froude number tend to 0 in a particular mutual rate while the Reynolds number tends to infinity. 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.