Strong solutions to a nonlinear fluid structure interaction system

Abstract

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 méthodes de résolution des problèmes aux limites non linéaires, Dunod, 1969] and considered in [V. Barbu, Z. Grujić, 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. Grujić, 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 ( Ω e ) and H 1 ( Ω e ) respectively.