On the classical solutions of two dimensional inviscid rotating shallow water system (Q619865)

A global existence and uniqueness of the mentioned problem are proved when the initial data are small enough and the initial vorticity is zero. The problem is reformulated into a system of symmetric quasilinear Klein-Gordon equations. The uniqueness and the existence of the solution are proved for a finite time interval, bounded in terms of a general initial data and relative vorticity. Some very interesting technical details concerning an important estimate of the solution, involving weighted Sobolev spaces, are given in the Appendix A.