We will prove local-in-time well-posedness for a fully dispersive Boussinesq system arising 
in the context of free surface water waves in two and three spatial dimensions.
Those systems can be seen as a weak nonlocal dispersive perturbation of the shallow-water system. 
Our method of proof relies on energy estimates and a compactness argument. 
However, due to the lack of symmetry of the nonlinear part, those traditional methods have to be supplemented
with the use of a modified energy in order to close the a priori estimates.

This talk is based on a joint work with Henrik Kalisch (University of Bergen)