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. (C) 2009 Elsevier Inc. All rights reserved.