Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain

Abstract

In this paper, we study a fluid--rigid-body interaction problem. The motion of the fluid is modeled by the Navier-Stokes equations, written in an unknown bounded domain depending on the displacement of the rigid body. Our main result yields existence and uniqueness of strong solutions. In the two-dimensional case, the solutions are global provided that the rigid body does not touch the boundary. In the three-dimensional case, we obtain local-in-time existence and global existence for small data. Moreover, we prove an asymptotic stability result.