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Derivation of a non-hydrostatic shallow water model; comparison with Saint-Venant and Boussinesq systems. (English) Zbl 1155.35405
Summary: From the free surface Navier-Stokes system, we derive the non-hydrostatic Saint-Venant system for the shallow waters including friction and viscosity. Based on an asymptotic analysis, the derivation leads to two formulations of growing complexity depending on the level of approximation chosen for the fluid pressure. The obtained models rely on formal estimates and are compared with the Boussinesq models.

MSC:
35Q30 Navier-Stokes equations
35Q35 PDEs in connection with fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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