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

TL;DR

This paper studies the conditions under which a solid body moving in a viscous compressible fluid within a bounded domain collides with its container, highlighting the role of boundary regularity in collision outcomes.

Contribution

It demonstrates that boundary roughness can lead to collision in finite time, and explores how boundary smoothness affects collision or no-collision scenarios.

Findings

Collision occurs in finite time for bodies with rough boundaries.

Smooth boundary bodies may not collide under certain conditions.

Boundary regularity influences collision behavior in viscous compressible fluids.

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.