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

Abstract

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

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