Strong solutions to a nonlinear fluid structure interaction system

In this paper, we prove the existence of local-in-time smooth solutions to the nonlinear fluid structure interaction model first introduced in [J.-L Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Dunod, 1969] and considered in [V. Barbu. Z. Grujic, I. Lasiecka, A. Tuffaha, Existence of the energy-level weak solutions for a nonlinear fluid-structure interaction model, in: Fluids and Waves, in: Contemp. Math., vol. 440, Amer. Math. Soc.. Providence, RI, 2007. pp. 55-82; V. Barbu, Z. Grujic, I. Lasiecka, A. Tuffaha, Smoothness of weak solutions to a nonlinear fluid-structure interaction model, Indiana Univ. Math. J. 57 (3) (2008) 1173-1207]. In particular, the strong solutions here are obtained given initial datum for the Navier-Stokes equation in the space H-1, and initial data for the wave equation w(0) and w(1) in the spaces H-2(Omega(e)) and H-1(Omega(e)) respectively. (C) 2009 Elsevier Inc. All rights reserved.