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arXiv · 0806.4504

Cauchy problem for viscous rotating shallow water equations

Chengchun Hao·Ling Hsiao·Hai-Liang Li
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Abstract

We consider the Cacuhy problem for a viscous compressible rotating shallow water system with a third-order surface-tension term involved, derived recently in the modelling of motions for shallow water with free surface in a rotating sub-domain. The global existence of the solution in the space of Besov type is shown for initial data close to a constant equilibrium state away from the vacuum. Unlike the previous analysis about the compressible fluid model without coriolis forces, the rotating effect causes a coupling between two parts of Hodge's decomposition of the velocity vector field, additional regularity is required in order to carry out the Friedrichs' regularization and compactness arguments.

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Chengchun Hao, Ling Hsiao, Hai-Liang Li. 2009-03-12. Cauchy problem for viscous rotating shallow water equations. https://doi.org/10.1016/j.jde.2009.09.008

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