Cauchy problem for viscous rotating shallow water equations
نویسندگان
چکیده
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 [18]. 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 [9, 15], 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.
منابع مشابه
Global Existence of Classical Solutions to Shallow Water Equations with Cauchy Data Containing Vacuum
In this paper, we investigate the singularity formulation of Cauchy problem to the viscous compressible rotating shallow water equations. We obtain the global existence of classical solutions with initial vacuum. In particular, the spatial measure of the set of vacuum can be arbitrarily large. 2000 Mathematics Subject Classification: 35Q35; 35M10; 76N10; 76U05.
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