Existence of strong solutions for the motion of an elastic structure in an incompressible viscous fluid

Abstract

In this paper we study a three-dimensional fluid–structure interaction problem. The motion of the fluid is modeled by the Navier–Stokes equations and we consider for the elastic structure a finite dimensional approximation of the equation of linear elasticity. The time variation of the fluid domain is not known a priori, so we deal with a free boundary value problem. Our main result yields the local in time existence and uniqueness of strong solutions for this system.