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

Fuente: arXiv
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Main Authors: Kreml, Ondřej, Nečasová, Šárka, Tang, Tong
Format: Preprint
Published: 2025
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author Kreml, Ondřej
Nečasová, Šárka
Tang, Tong
author_facet Kreml, Ondřej
Nečasová, Šárka
Tang, Tong
contents Inspired by Abbatiello, Feireisl and Novotný, 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_20476
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On dissipative turbulent solutions to the compressible anisotropic Navier-Stokes equations in unbounded domains
Kreml, Ondřej
Nečasová, Šárka
Tang, Tong
Analysis of PDEs
35Q30, 76N10
Inspired by Abbatiello, Feireisl and Novotný, 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.
title On dissipative turbulent solutions to the compressible anisotropic Navier-Stokes equations in unbounded domains
topic Analysis of PDEs
35Q30, 76N10
url https://arxiv.org/abs/2510.20476