On a non-homogeneous bi-layer shallow-water problem: smoothness and uniqueness results Original Research Article

In this paper, we present several results for a non-homogeneous bi-layer shallow-water model in depth-mean velocity formulation. The homogeneous case was studied in (Nonlinear Anal.: Real World Appl. 4(1) (2003) 139–171). In (On a non-homogeneous bi-layer shallow water problem: an existence theorem, Diff. and Integral Equations 17 (9–10) (2004) 1175–1200) we proved the existence of a solution for the non-homogeneous problem and now we give some smoothness and uniqueness results. The main difficulties in the non-homogeneous case arise from the treatment of the boundary terms.