Rigid body in compressible flow with general inflow-outflow boundary data

We study the motion of a rigid body within a compressible, isentropic, and viscous fluid contained in a fixed bounded domain Ω ⊂ R³. The fluid's behavior is described by the Navier-Stokes equations, while the motion of the rigid body is governed by ordinary differential equations representing the conservation of linear and angular momentum. We prescribe a time-independent fluid velocity along the boundary of Ω and a time-independent fluid density at the inflow boundary of Ω. Additionally, we assume a no-slip boundary condition at the interface between the fluid and the rigid body. We prove existence of a weak solution to the given problem within a time interval where the rigid body does not touch the boundary ∂Ω.