Mathematical Analysis of the Motion of a Rigid Body in a Compressible Navier-Stokes-Fourier Fluid

TL;DR

This paper establishes the existence of strong solutions for the motion of a rigid body in a heat-conducting gas modeled by compressible Navier-Stokes-Fourier equations, using maximal regularity and operator theory techniques.

Contribution

It provides a rigorous mathematical analysis proving local and global existence of solutions for the coupled fluid-solid system with heat conduction, a novel result in this context.

Findings

Existence of strong solutions in an Lp-Lq framework.

Global solutions for small initial data.

Use of R-sectoriality and maximal regularity methods.

Abstract

We study an initial and boundary value problem modelling the motion of a rigid body in a heat conducting gas. The solid is supposed to be a perfect thermal insulator. The gas is described by the compressible Navier-Stokes-Fourier equations, whereas the motion of the solid is governed by Newton's laws. The main results assert the existence of strong solutions, in an L p-L q setting, both locally in time and globally in time for small data. The proof is essentially using the maximal regularity property of associated linear systems. This property is checked by proving the R-sectoriality of the corresponding operators, which in turn is obtained by a perturbation method.