SEVERAL MODELS FOR WAVE-STRUCTURE INTERACTIONS (Workshop on Nonlinear Water Waves)SEVERAL MODELS FOR WAVE‐STRUCTURE INTERACTIONS

We present in this note two mathematical problems related to the study of floating objects. In the first one, the fluid is described through the one-dimensional nonlinear shallow water equations; the main difficulty is to solve the free boundary problem that consists in finding the location of the contact points between the surface of the water and the floating object. In the second one, the lateral sides of the object are assumed to be vertical, so that that the coordinates of the contact points are known, but we consider a fluid described by a Boussinesq model. The problem can be reduced to a transmission problem and the presence of the dispersive terms requires the development of new tools. We also describe the main points of the analysis and refer to [9] and [4] respectively for full details