Cauchy problem for viscous shallow water equations with surface tension

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May 2010, 13(3): 593-608. doi: 10.3934/dcdsb.2010.13.593

Cauchy problem for viscous shallow water equations with surface tension

1.	Institute of Mathematics, Academy of Mathematics & Systems Science, CAS, Beijing 100080

Received September 2008 Revised January 2010 Published February 2010

Abstract
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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.

Keywords: Shallow water equation with surface tension, global-in-time solution., homogeneous Besov space, Littlewood-Paley decomposition.

Mathematics Subject Classification: Primary: 35Q35; Secondary: 76N1.

Citation: Chengchun Hao. Cauchy problem for viscous shallow water equations with surface tension. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 593-608. doi: 10.3934/dcdsb.2010.13.593

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