Dispersive estimates for full dispersion KP equations

Abstract

We prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev-Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev-Petviashvili equations. The proof of these estimates combines the stationary phase method with sharp asymptotics on asymmetric Bessel functions, which may be of independent interest. As a consequence, we prove that the initial value problem associated to the Full Dispersion Kadomtsev-Petviashvili is locally well-posed in $H^s({\mathbb{R}}^2)$, for $s>\frac{7}{4}$, in the capillary-gravity setting.

29 pages, 3 figures

Cited by in corpus (1)

• On the full dispersion Kadomtsev-Petviashvili equations for dispersive elastic waves