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In this paper we study a coupled system modeling the movement of a deformablesolid immersed in a fluid. For the solid we consider a given deformation thathas to obey several physical constraints. The motion of the fluid is modeled bythe incompressible Navier-Stokes equations in a time-dependent bounded domainof $\R^3$, and the solid satisfies the Newton's laws. Our contribution consistsin adapting and completing some results of ARMA 2008 in dimension 3, in aframework where the regularity of the deformation of the solid is limited. Werewrite the main system in domains which do not depend on time, by using a newmeans of defining a change of variables, and a suitable change of unknowns. Westudy the corresponding linearized system before setting a local-in-timeexistence result. Global existence is obtained for small data, and inparticular for deformations of the solid which are arbitrarily close to theidentity.

Existence of 3D strong solutions for a system modeling a deformable solid inside a viscous incompressible fluid