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.
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Muriel Boulakia, Erica L. Schwindt, Takéo Takahashi, Existence of strong solutions for the motion of an elastic structure in an incompressible viscous fluid. Interfaces Free Bound. 14 (2012), no. 3, pp. 273–306DOI 10.4171/IFB/282