Shallow water model for lakes with friction and penetration

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.


{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.}