Low Mach number limit on perforated domains for the evolutionary Navier-Stokes-Fourier system

TL;DR

This paper studies the low Mach number limit of the Navier-Stokes-Fourier system in perforated domains, establishing convergence to the Oberbeck-Boussinesq approximation and demonstrating the weak-strong uniqueness principle.

Contribution

It identifies dissipative solutions as a low Mach limit and proves strong convergence via weak-strong uniqueness in perforated domains.

Findings

Dissipative solutions correspond to the low Mach limit.

Strong convergence to the Oberbeck-Boussinesq system is established.

Weak-strong uniqueness principle is proved for the system.

Abstract

We consider the Navier-Stokes-Fourier system describing the motion of a compressible, viscous and heat-conducting fluid on a domain perforated by tiny holes. First, we identify a class of dissipative solutions to the Oberbeck-Boussinesq approximation as a low Mach number limit of the primitive system. Secondly, by proving the weak-strong uniqueness principle, we obtain strong convergence to the target system on the lifespan of the strong solution.