Weak solutions to the barotropic Navier-Stokes system with slip boundary conditions in time dependent domains

TL;DR

This paper establishes the existence of global weak solutions for the compressible barotropic Navier-Stokes equations in time-dependent domains with slip boundary conditions, using penalization techniques.

Contribution

It introduces a novel penalization approach to handle boundary behavior, viscosity, and pressure in weak formulations for time-dependent domains.

Findings

Global-in-time weak solutions are proven to exist.

The method effectively manages slip boundary conditions in dynamic domains.

The approach advances understanding of compressible fluid flows in complex geometries.

Abstract

We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak formulation. Global-in-time weak solutions are obtained.