Viscosity effect on the degenerate lake equations. (January 2017)

• Record Type: Journal Article
• Authors: Al Taki, Bilal
• Is Part Of: Nonlinear analysis. Volume 148(2017)
• Page Start: 30
• Page End: 60
• Publication Date: 2017-01
• Subjects: 35Q30 -- 76D03 -- 76D05 -- 35B25; Viscous lake equations -- Inviscid limit -- Power-type weights -- Weighted Sobolev spaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.09.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper concerns the effect of viscosity on the degenerate lake equations (anelastic limit) when the bottom topography vanishes on the shore. We establish the existence and uniqueness of a global weak solutions for various choices of viscosity term in weighted Sobolev spaces where the weight is assumed to be a power type weight . Our solution is constructed by adapting carefully the known works on the incompressible Navier–Stokes equations in unweighted context. Finally we study, in one case, the vanishing viscosity limit when the solution of the inviscid lake equations is regular enough generalizing the results by Martino et al. (2001) to the degenerate case.