Asymptotic profile for the interaction of a rigid ball and an incompressible viscous fluid

Abstract

In this paper, we study the large time behavior of the solutions of the Stokes fluid-solid system. We compute the asymptotic expansion of the solution for Lq integrable initial data U0. We show that the asymptotic profile of the solution is a linear combination of the Stokes fundamental solution for the data with extra condition |x|U0∈L1. We also show that L1 integrability of the solution is strongly related to the net force exerted by the fluid on the boundary of the solid.