Compressible Navier--Stokes system with the hard sphere pressure law in an exterior domain

TL;DR

This paper proves the existence of weak solutions for the compressible Navier-Stokes equations with a hard sphere pressure law around an obstacle, considering non-zero velocity and density at infinity, relevant for physical and industrial applications.

Contribution

It establishes the existence of weak solutions for a complex fluid model in an exterior domain with realistic boundary conditions, advancing mathematical understanding of such systems.

Findings

Existence of weak solutions proved

Applicable to physical and industrial scenarios

Handles non-zero velocity and density at infinity

Abstract

We consider the motion of compressible Navier-Stokes fluids with the hard sphere pressure law around a rigid obstacle when the velocity and the density at infinity are non zero. This kind of pressure model is largely employed in various physical and industrial applications. We prove the existence of weak solution to the system in the exterior domain.