Long-time existence for a whitham boussinesq system in two dimensions

This paper is concerned with a two-dimensional Whitham–Boussinesq system modeling surface waves of an inviscid incompressible fluid layer. We prove that the associated Cauchy problem well-posed for initial data low regularity, existence time scale [Formula: see text], where text] and are small parameters related to level dispersion nonlinearity, respectively. In particular, in KdV regime text]}, order text]. The main ingredients proof frequency loacalized dispersive estimates bilinear Strichartz depend on parameter