Existence for an unsteady fluid-structure interaction problem

We study the well-posedness of an unsteady fluid-structure interaction problem. We consider a viscous incompressible flow, which is modelled by the Navier-Stokes équations. The structure is a collection of rigid moving bodies, The fluid domain dépends on time and is defined by the position of the structure, itself resulting rrom a stress distribution coming from the fluid. The problem is then nonlinear and the équations we deal with are coupled. We prove its local solvability in time through two fixed point procedures. Mathematics Subject Classification. 76D05, 35Q30, 73K70. Received: April 9, 1999. Revised: October 7, 1999.