Shallow Water Model for Lakes with Friction and Penetration

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Abstract

We deduce a shallow water model, describing the motion of the fluid in a lake, assuming inflow-outflow effects acrossthe bottom. This model arises from the asymptotic analysis of the 3D dimensional Navier-Stokes equations. We prove theglobal in time existence result for thismodel in a bounded domain taking the nonlinear slip/friction boundary conditionsto describe the inflows and outflows of the porous coast and the rivers. The solvability is shown in the class of solutionswith Lp-bounded vorticity for any given p∈(1,∞].
Original languageUnknown
Pages (from-to)687-703
JournalMATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume33
Issue number6
DOIs
Publication statusPublished - 1 Jan 2010

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