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Shallow water model for lakes with friction and penetration. (English) Zbl 1200.35210
The authors deduce a shallow water model, describing the motion of the fluid in a lake, assuming inflow-outflow effects across the bottom. This model arises from the asymptotic analysis of the 3D dimensional Navier-Stokes equations. The authors prove the global in time existence result for this model in a bounded domain taking the nonlinear slip/friction boundary conditions to describe the inflows and outflows of the porous coast and the rivers.

MSC:
35Q30 Navier-Stokes equations
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76B47 Vortex flows for incompressible inviscid fluids
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