Global Existence of Classical Solutions in the Dissipative Shallow Water Equations

Abstract

An energy method of Matsumura and Nishida is used to prove the global temporal existence of classical solutions in the dissipative shallow water equations on a spatially periodic horizontal domain. This requires the external forcing, the initial data and the initial first order time derivatives to be sufficiently small. The result is related to the data initialization problem in numerical weather prediction, and extends a local existence result of Bui An Ton for the same equations.