Premium
Shallow water model for lakes with friction and penetration
Author(s) -
Chemetov N. V.,
Cipriano F.,
Gavrilyuk S.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1185
Subject(s) - inflow , bounded function , outflow , mathematics , nonlinear system , vorticity , boundary value problem , nonlinear model , domain (mathematical analysis) , slip (aerodynamics) , shallow water equations , mathematical analysis , mechanics , geology , vortex , physics , oceanography , thermodynamics , quantum mechanics
We deduce a shallow water model, describ‐ing the motion of the fluid in a lake, assuming inflow–outflow effects across thebottom. This model arises from the asymptotic analysis of the 3D dimensionalNavier–Stokes equations. We prove the global in time existence result for thismodel in a bounded domain taking the nonlinear slip/friction boundary conditions to describe the inflows and outflows of the porous coast and the rivers. Thesolvability is shown in the class of solutions with L p ‐bounded vorticity for any given p ∈( 1 ,∞]. Copyright© 2009 John Wiley & Sons, Ltd.