Inviscid incompressible limits under mild stratification: A rigorous derivation of the Euler-Boussinesq system

TL;DR

This paper rigorously derives the Euler-Boussinesq system as the limit of the full Navier-Stokes-Fourier equations under small Mach number and large Reynolds and Peclet numbers, with ill-prepared initial data.

Contribution

It provides a rigorous mathematical derivation of the Euler-Boussinesq system from the Navier-Stokes-Fourier equations in a singular limit with weak solutions.

Findings

Identification of the Euler-Boussinesq system as the singular limit

Handling of ill-prepared initial data in the derivation

Extension of the analysis to unbounded 3D domains

Abstract

We consider the full Navier-Stokes-Fourier system in the singular regime of small Mach and large Reynolds and Peclet numbers, with ill prepared initial data on an unbounded domain in the three dimensional Euclidean space with a compact boundary. We perform the singular limit in the framework of weak solutions and identify the Euler-Boussinesq system as the target problem.