A shallow-water sedimentation model with friction and Coriolis: An existence theorem

We present an existence theorem of a two-dimensional sedimentation model coupling a shallow water system with a sediment transport equation. The shallow water system includes Coriolis and friction terms. A Galerkin method is used to obtain a finite-dimensional problem which is solved using a Brouwer fixed point theorem. We prove that the limits of the resulting solution sequences satisfy the model equations.