# Well-posedness for a dispersive system of the Whitham-Boussinesq type

## TL;DR

This paper establishes local and global well-posedness results for a specific Whitham-Boussinesq system modeling surface waves, using dispersive estimates and Hamiltonian conservation, especially at low regularity levels.

## Contribution

It introduces new dispersive and Strichartz estimates for the system and proves well-posedness at low regularity, extending previous results in the field.

## Key findings

- Local well-posedness at low regularity
- Global well-posedness for small initial data in 1D
- Dispersive estimates for the system

## Abstract

We regard the Cauchy problem for a particular Whitham-Boussinesq system modelling 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.