The multilayer shallow water system in the limit of small density contrast (Q2817257)

The authors study the inviscid multilayer Saint-Venant system in the limit of small density contrast. They show that, under reasonable hyperbolicity conditions on the flow and a smallness assumption on the initial surface deformation, the system is well-posed on a large time interval. By studying the asymptotic limit, they provide a rigorous justification of the widely used rigid-lid and Boussinesq approximations for multilayered shallow water flows. The asymptotic behaviour is similar to that of the incompressible limit for Euler equations, in the sense that there exists a small initial layer in time for ill-prepared initial data, accounting for rapidly propagating ``acoustic'' waves which interacts weakly with the ``incompressible'' component.