Cauchy problem for viscous shallow water equations with surface tension

Chengchun Hao

doi:10.3934/dcdsb.2010.13.593

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2010, Volume 13, Issue 3: 593-608. Doi: 10.3934/dcdsb.2010.13.593

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Cauchy problem for viscous shallow water equations with surface tension

Chengchun Hao^1,

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

Received: August 31, 2008

Revised: December 31, 2009

Published: September 2010

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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.

Keywords:

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

Mathematics Subject Classification: Primary: 35Q35; Secondary: 76N10.

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