Inviscid incompressible limits of the full Navier-Stokes-Fourier system

TL;DR

This paper investigates the behavior of the full Navier-Stokes-Fourier system under singular limits involving small Mach and large Reynolds and Peclet numbers, demonstrating convergence to the Euler-Boussinesq approximation with ill-prepared initial data.

Contribution

It establishes the inviscid incompressible limit of the Navier-Stokes-Fourier system in three dimensions with ill-prepared initial data, linking it to the Euler-Boussinesq system.

Findings

Convergence of the Navier-Stokes-Fourier system to Euler-Boussinesq in the specified limit

Handling of ill-prepared initial data in the analysis

Identification of the limit system as Euler-Boussinesq

Abstract

We consider the full Navier-Stokes-Fourier system in the singular limit for the small Mach and large Reynolds and Peclet numbers, with ill prepared initial data on the three dimensional Euclidean space. The Euler-Boussinesq approximation is identified as the limit system.