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 finitedimensional 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. 2010 Mathematics Subject Classification: Primary 74F10, 76D03; Secondary 35R35, 35Q30, 37N15, 76D05. © 2012 European Mathematical Society.