1. Introduction

This paper deals with the mathematical and numerical analysis of problems dealing with unsteady fluid-structure interaction phenomena. These phenomena are of major importance for aerospace, mechanical or biomedical applications, and thus have been studied by many authors over the past few years from different points of view (theory, numerical analysis and simulations). The problem is to describe the evolution of a viscous fluid coupled with a moving structure. The fluid can be compressible or incompressible, and the structure can be rigid or elastic. Several conditions determine the coupling between the two media at their interface. First, the kinematic condition states that the fluid velocity and the structure velocity are equal. The second coupling condition traduces the action-reaction principle. The interaction is not reduced to these only transmission conditions since, in most interesting cases where the deformations of the structure are large enough, one can not neglect the variation of the fluid domain. We thus have to solve a problem defined (at least for the fluid part) over a time dependent domain. We focus here on the analysis and numerical analysis of the fluid-structure interaction problems in the case where the deformation of the fluid domain is actually part of the unknown. We refer to [MOR 92] for a study of the vibrations of coupled problems in which the domain is fixed.

Section 2...