Interfaces and Free Boundaries


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Volume 14, Issue 3, 2012, pp. 273–306
DOI: 10.4171/IFB/282

Published online: 2012-11-07

Existence of strong solutions for the motion of an elastic structure in an incompressible viscous fluid

Muriel Boulakia[1], Erica L. Schwindt[2] and Takéo Takahashi[3]

(1) Université Pierre et Marie Curie, Paris, France
(2) Universidad de Chile, Santiago, Chile
(3) Université Henri Poincaré, Vandoeuvre-Les-Nancy, France

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.

Keywords: Fluid-structure interaction, existence and uniqueness of strong solutions, incompressible Navier–Stokes equations, deformable structure

Boulakia Muriel, Schwindt Erica, Takahashi Takéo: Existence of strong solutions for the motion of an elastic structure in an incompressible viscous fluid. Interfaces Free Bound. 14 (2012), 273-306. doi: 10.4171/IFB/282