Sur un problème de shallow water bicouche avec conditions aux limites de Dirichlet

We present in this Note an existence result for a bi-layer shallow water problem, with Dirichlet boundary conditions. The main difficulty arises from the terms coupling the two layers. To handle these, we must couple the natural energy estimate with an estimation of the thickness in L2(Q). To obtain this L2-estimate, we introduce the Stokes operator and we use results for Hardy spaces to treat the nonlinear terms. To cite this article: F. Flori et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).