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In this paper we address a particular fluid-solid interaction problem inwhich the solid object is lying at the bottom of a layer of fluid and movesunder the forces created by waves travelling on the surface of this layer. Moreprecisely, we consider the water waves problem in a fluid of fixed depth with aflat bottom topography and with an object lying on the bottom, allowed to movehorizontally under the pressure forces created by the waves. After establishingthe physical setting of the problem, namely the dynamics of the fluid and themechanics of the solid motion, as well as analyzing the nature of the coupling,we examine in detail two particular shallow water regimes: the case of the(nonlinear) Saint-Venant system, and the (weakly nonlinear) Boussinesq system.We prove an existence and uniqueness theorem for the coupled system in bothcases. Using the particular structure of the coupling terms we are able to gobeyond the standard scale for the existence time of solutions to the Boussinesqsystem with a moving bottom.

Wave-structure interaction for long wave models in the presence of a freely moving body on the bottom