On the motion of rigid bodies in a perfect fluid

TL;DR

This paper demonstrates that in a perfect compressible fluid, the motion of rigid bodies can have infinitely many weak solutions that are time-reversible, despite satisfying entropy conditions.

Contribution

It introduces the use of convex integration to show the existence of infinitely many weak solutions with prescribed rigid body motion in a compressible fluid.

Findings

Existence of infinitely many weak solutions for rigid bodies in a perfect fluid

Solutions are time-reversible despite entropy conditions

Method employs convex integration to construct solutions

Abstract

We consider the problem of motion of several rigid bodies immersed in a perfect compressible fluid. Using the method of convex integration we establish the existence of infinitely many weak solutions with {\it a priori} prescribed motion of rigid bodies. In particular, the dynamics is completely \emph{time--reversible} at the motion of rigid bodies although the solutions comply with the standard entropy admissibility criterion.