On a nonlinear fluid-structure interaction problem defined on a domain depending on time

A fluid-structure coupling problem for which the structure occupies a portion of the fluid domain boundary is considered. Coupling is expressed by the hypothesis on normal velocity continuity at the boundary and by introducing a parietal pressure term in the equation of structure behavior. Under conditions of weak disturbances, it is assumed that the fluid occupies a fixed domain. However, this assumption leads to difficulties which do not allow proof of well-posedness for general cases in which nonlinear conservation equations. Nevertheless, by considering the structure's displacement within the fluid domain, it can be proven that the problem is well posed for a bidimensional situation.