On dissipative turbulent solutions to the compressible anisotropic Navier-Stokes equations in unbounded domains

TL;DR

This paper establishes the global existence of dissipative turbulent solutions for the compressible anisotropic Navier-Stokes equations in unbounded domains, relaxing previous assumptions and applicable to geophysical contexts.

Contribution

It introduces a broader class of solutions for anisotropic Navier-Stokes equations on unbounded domains, extending prior results and proving weak-strong uniqueness.

Findings

Existence of dissipative turbulent solutions in unbounded domains.

Relaxed assumptions on anisotropic tensor coefficients.

Proved weak-strong uniqueness property.

Abstract

Inspired by Abbatiello, Feireisl and Novotn\'y, we prove the global existence of dissipative turbulent solution for the compressible Navier-Stokes equations with anisotropic viscous stress tensor on unbounded domain. Our work complements the result of Bresch and Jabin, where the authors used the new compactness method to prove the existence of a weak solution to the same system in $\mathbb{T}^3$. By virtue of the concept of dissipative turbulent solutions, we are able to relax assumptions on the anisotropic tensor coefficients and the pressure law coefficient. We point out that we establish the existence result on a large class of unbounded domains, which is more conform to geophysical context. We also prove the weak-strong uniqueness property of acquired dissipative turbulent solutions.