On the motion of a compressible viscous fluid driven by time periodic inflow/outflow boundary conditions

TL;DR

This paper proves the existence of time periodic weak solutions for the barotropic Navier-Stokes equations describing a compressible viscous fluid under periodic boundary conditions, extending understanding of fluid behavior in bounded domains.

Contribution

It demonstrates the existence of time periodic solutions for the Navier-Stokes system with periodic boundary conditions, a novel result for this class of problems.

Findings

Existence of time periodic weak solutions

Solutions satisfy the energy inequality

Applicable to bounded domains with periodic inflow/outflow

Abstract

We consider the barotropic Navier-Stokes system describing the motion of a compressible viscous fluid confined to a bounded domain driven by time periodic inflow/outflow boundary conditions. We show that the problem admits a time periodic solution in the class of weak solutions satisfying the energy inequality.