Cauchy problem for viscous rotating shallow water equations

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.