Cauchy problem for viscous shallow water equations with surface tension

Chengchun Hao

Type: Article

Publication Date: 2010-01-01

Citations: 2

DOI: https://doi.org/10.3934/dcdsb.2010.13.593

Abstract

We are concerned with the Cauchy problem for a viscous shallow water system with a third-order surface-tension term. The global existence and uniqueness of the solution in the space of Besov type is shown for the initial data close to a constant equilibrium state away from the vacuum by using the Friedrich's regularization and compactness arguments.

Locations

Discrete and Continuous Dynamical Systems - B - View - PDF

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+	New thoughts on Besov spaces	1976	Jaak Peetre
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+	Global existence in critical spaces for compressible Navier-Stokes equations	2000	Raphaël Danchin
+	Existence and Uniqueness of a Classical Solution of an Initial-Boundary Value Problem of the Theory of Shallow Waters	1981	Bùi An Tôn
+	Global Existence of Classical Solutions in the Dissipative Shallow Water Equations	1985	Peter E. Kloeden
+ PDF Chat	The Cauchy problem for viscous shallow water equations	2005	Weike Wang Chao-Jiang Xu
+ PDF Chat	Global Existence for the Cauchy Problem for the Viscous Shallow Water Equations	1998	Linda Sundbye
+	Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects	2006	Fabien Marche