Well-Posedness for a Dispersive System of the Whitham-Boussinesq Type

Abstract

We regard the Cauchy problem for a particular Whitham--Boussinesq system modeling surface waves of an inviscid incompressible fluid layer. We are interested in well-posedness at a very low level of regularity. We derive dispersive and Strichartz estimates and implement them together with a fixed point argument to solve the problem locally. Hamiltonian conservation guarantees global well-posedness for small initial data in the one dimensional settings.