Dispersive estimates for nonhomogeneous radial phases: an application to weakly dispersive equations and water wave models

We study linear dispersive equations in dimension one and two for a class of radial nonhomogeneous phases. L 1 $\to$ L $\mathrm{\infty }$ type estimates, Strichartz estimates, local Kato smoothing and Morawetz type estimates are provided. We then apply our results to different water wave models.