论文标题
完整色散KP方程的分散估算
Dispersive estimates for full dispersion KP equations
论文作者
论文摘要
我们证明了David Lannes引入的完整分散kadomtsev-petviashvili的线性部分的几个分散估计值，以克服古典kadomtsev-petviashvili方程的一些缺点。这些估计值的证据将固定相法与尖锐的渐近渐近型结合了在不对称的贝塞尔函数上，这可能具有独立感兴趣。结果，我们证明了与完整分散kadomtsev-petviashvili相关的初始值问题在$ h^s（\ mathbb r^2）$中，以$ s> \ frac74 $，在毛细血管 - 毛细笔设置中。
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 $s>\frac74$, in the capillary-gravity setting.
