Cauchy problem for viscous rotating shallow water equations |
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Authors: | Chengchun Hao Ling Hsiao |
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Affiliation: | a Institute of Mathematics, Academy of Mathematics & Systems Science, CAS, Beijing 100190, PR China b Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, PR China c Department of Mathematics, Capital Normal University, Beijing 100037, PR China |
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Abstract: | We consider the Cauchy problem for a viscous compressible rotating shallow water system with a third-order surface-tension term involved, derived recently in the modeling of motions for shallow water with free surface in a rotating sub-domain Marche (2007) [19]. 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, see for instance Danchin (2000) [10], Haspot (2009) [16], the rotating effect causes a coupling between two parts of Hodge's decomposition of the velocity vector field, and additional regularity is required in order to carry out the Friedrichs' regularization and compactness arguments. |
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Keywords: | Viscous compressible rotating shallow water system Cauchy problem Global well-posedness Besov spaces |
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