A regularity result for a solid–fluid system associated to the compressible Navier–Stokes equations

Abstract

In this paper we deal with a fluid-structure interaction problem for a compressible fluid and a rigid structure immersed in a regular bounded domain in dimension 3. The fluid is modelled by the compressible Navier–Stokes system in the barotropic regime with no-slip boundary conditions and the motion of the structure is described by the usual law of balance of linear and angular moment.The main result of the paper states that, for small initial data, we have the existence and uniqueness of global smooth solutions as long as no collisions occur. This result is proved in two steps; first, we prove the existence and uniqueness of local solution and then we establish some a priori estimates independently of time.