Derivation of geostrophic equations as a rigorous limit of compressible rotating and heat conducting fluids with the general initial data

Abstract

We investigate a distinguished low Mach and Rossby - high Reynolds and Peclet number singular limit in the complete Navier-Stokes-Fourier system towards a strong solution of a geostrophic system of equations. The limit is effectuated in the context of weak solutions with ill prepared initial data. The main tool in the proof is based on the relative energy method.