Shallow water model for lakes with friction and penetration

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.