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

We study here the two dimensional motion of an elastic body immersed in an incompressible viscous fluid. The body and the fluid are contained in a fixed bounded set Ω . We show the existence of a weak solution for regularized elastic deformations as long as elastic deformations are not too important and no collisions occur. A complete proof is given by Boulakia in existence d'une solution faible pour un problème d'interaction fluide visqueux incompressible-solide élastique (prepublication 104, UVSQ, 2003).