Motion of several rigid bodies in a compressible fluid – mixed case

Abstract

In this article we show local-in-time existence of a weak solution to a system of partial differential equations describing the evolution of a compressible isentropic fluid which contains several rigid bodies. The fluid-structure interaction is incorporated by the Navier-slip boundary condition at the interface of the fluid and the rigid bodies. At the boundary of the fluid’s container, we assume Dirichlet boundary conditions. This work follows an earlier article of the same authors regarding the evolution of a compressible fluid that contains one rigid body and assumes Navier-slip boundary conditions at the interface as well as at the boundary of the container. The novelties comprise a new bound on the maximal time, for which we can prove existence of weak solutions, different test functions and a different extension of the fluid velocity from the fluid domain to the whole container.