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Citation:

Chemetov, N. V., F. Cipriano, and S. Gavrilyuk. "Shallow water model for lakes with friction and penetration." MATHEMATICAL METHODS IN THE APPLIED SCIENCES. 33 (2010): 687-703.

Abstract:

{We 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. We 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. The solvability is shown in the class of solutions with L(p)-bounded vorticity for any given p is an element of (1, infinity). Copyright (C) 2009 John Wiley & Sons, Ltd.}

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