On the well-posedness of the Galerkin semidiscretization of the periodic initial-value problem of the Serre equations

Abstract

We consider the periodic initial-value problem for the Serre equations of water-wave theory and its semidiscrete approximation in the space of smooth periodic polynomial splines. We prove that the semidiscrete problem is well posed, locally in time, and satisfies a discrete positivity property for the water depth.