Collision/no-collision results of a solid body with its container in a 3D compressible viscous fluid

Abstract

We consider a bounded domain $\Omega \subset R^3$ and a rigid body $S\left(t\right)\subset \Omega$ moving inside a viscous compressible Newtonian fluid. We exploit the body's roughness to establish that the solid collides with its container within a finite time. We investigate the case when the boundary of the body is of $C^{1,\alpha }$-regularity and show that collision can happen for some suitable range of α. We also discuss some no-collision results for the smooth body case when an additional control is added.