Compressible fluid inside a linear oscillator

TL;DR

This paper establishes the existence of weak solutions for a model describing a Newtonian compressible fluid inside a linear oscillator with one degree of freedom, using advanced mathematical theory.

Contribution

It applies Feireisl-Lions theory to prove weak solutions for a fluid-structure interaction system involving a compressible fluid and a moving domain.

Findings

Existence of weak solutions demonstrated

Mathematical framework for fluid-oscillator interaction established

Applicable to systems with one degree of freedom

Abstract

We use Feireisl-Lions theory to deduce the existence of weak solutions to a system describing the dynamics of a linear oscillator containing a Newtonian compressible fluid. The appropriate Navier-Stokes equation is considered on a domain whose movement has one degree of freedom. The equation is paired with the Newton law and we assume a no-slip boundary condition.