  In this article we address some issues related to the initial value problems
for a rotating shallow water hyperbolic system of equations and the diffusive
regularization of this system. For initial data close to the solution at rest,
we establish the local existence and the uniqueness of a solution to the
hyperbolic system, as well as the global existence of a solution to the
regularized system. In order to prove this, we use suitable variables that
symmetrize the system.
