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A shallow water model with eddy viscosity for basins with varying bottom topography. (English) Zbl 0999.76033

Summary: We consider the motion of an incompressible fluid confined to a shallow basin with varying bottom topography. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three-dimensional eddy viscosity model plays a critical role in ensuring that the resulting shallow water model dissipates energy.

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76D27 Other free boundary flows; Hele-Shaw flows
35Q30 Navier-Stokes equations
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