Strong solutions to a nonlinear fluid structure interaction system

AbstractIn 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 H1, and initial data for the wave equation w0 and w1 in the spaces H2(Ωe) and H1(Ωe) respectively