Strong solutions for a fluid structure interaction system

Abstract

We consider the structure-interaction model, introduced by J.-L. Lions, describing the interaction of an elastic body and an incompressible fluid. Recently, many works have addressed well posedness for this model. In this paper, we prove local existence of strong solutions under the initial condition $(u_0,w_0,w_1)\in H^{1}\times H^{3/2+k}\times H^{1/2+k}$ for every $k>0$ sufficiently small and where $u_0$, $w_0$, and $w_1$ are the initial velocity of the fluid, initial displacement of the body, and the initial velocity of the body respectively. We also propose new alternative matching stress boundary conditions for this model.

Article information

Source
Adv. Differential Equations Volume 15, Number 3/4 (2010), 231-254.

Dates
First available in Project Euclid: 18 December 2012