Existence of weak solutions for models of general compressible viscous fluids with linear pressure

TL;DR

This paper proves the existence of weak solutions for a general compressible viscous fluid model with linear pressure and nonlinear viscous stress, expanding understanding of fluid dynamics under these conditions.

Contribution

It establishes the existence of dissipative and weak solutions for complex fluid models with linear pressure and nonlinear viscosity, under specific conditions.

Findings

Existence of dissipative solutions established

Conditions for weak solutions identified

Framework for analyzing compressible viscous fluids developed

Abstract

In this work we will focus on the existence of weak solutions for a system describing a general compressible viscous fluid in the case of the pressure being a linear function of the density and the viscous stress tensor being a non-linear function of the symmetric velocity gradient. More precisely, we will first prove the existence of dissipative solutions and study under which conditions it is possible to guarantee the existence of weak solutions.