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Shallow water model for lakes with friction and penetration

2009; Wiley; Volume: 33; Issue: 6 Linguagem: Inglês

10.1002/mma.1185

1099-1476

Nikolai V. Chemetov, Fernanda Cipriano, Sergey Gavrilyuk,

Nonlinear Partial Differential Equations

Mathematical Methods in the Applied SciencesVolume 33, Issue 6 p. 687-703 Research Article Shallow water model for lakes with friction and penetration N. V. Chemetov, Corresponding Author N. V. Chemetov [email protected] CMAF/Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, PortugalCMAF/Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal===Search for more papers by this authorF. Cipriano, F. Cipriano GFM e Dep. de Matemática FCT-UNL, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, PortugalSearch for more papers by this authorS. Gavrilyuk, S. Gavrilyuk Marseille University and CNRS UMR 6595, IUSTI, Marseille, FranceSearch for more papers by this author N. V. Chemetov, Corresponding Author N. V. Chemetov [email protected] CMAF/Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, PortugalCMAF/Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal===Search for more papers by this authorF. Cipriano, F. Cipriano GFM e Dep. de Matemática FCT-UNL, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, PortugalSearch for more papers by this authorS. Gavrilyuk, S. Gavrilyuk Marseille University and CNRS UMR 6595, IUSTI, Marseille, FranceSearch for more papers by this author First published: 29 July 2009 https://doi.org/10.1002/mma.1185Citations: 7AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract We deduce a shallow water model, describ- ing 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 Lp-bounded vorticity for any given p∈(1,∞]. Copyright © 2009 John Wiley & Sons, Ltd. Citing Literature Volume33, Issue6April 2010Pages 687-703 RelatedInformation