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

Abstract

We consider a bounded domain $\Omega\subset\mathbb R^3$ and a rigid body $\mathcal{S}(t)\subset\Omega$ moving inside a viscous compressible Newtonian fluid. We exploit the roughness of the body to show that the solid collides its container in 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 $\alpha$. We also discuss some no-collision results for the smooth body case.