Existence of weak solutions for an interaction problem between an elastic structure and a compressible viscous fluid

Abstract

In this article, we are interested by the three-dimensional motion of an elastic structure immersed in a viscous compressible fluid. The fluid and the structure are contained in a fixed bounded set. To describe the structure motion, we choose an Eulerian point of view and we strongly regularize the equation of the solid motion in order to get additional estimates on the elastic deformations. Our maim result is an existence result of weak solutions defined as long as no collisions occur and as long as conditions of non-interpenetration and of preservation of orientation are satisfied.