数学研究所

数学科学全国重点实验室

调和分析及其应用研究中心

学术报告

偏微分方程研讨班

Speaker: Prof. Nikolay Tzvetkov (ENS Lyon)

Inviter: 范晨捷 副研究员

Language: English

Title:  On quasi-linear versions of the KP-II equation 

Time&Venue: 2025年5月21日（星期三）16:00-17:00& 南楼N224

Abstract: The Kadomtsev-Petviashvili equations (KP-I and KP-II) are modelling the propagation of small amplitude long waves in the presence of transverse perturbations. In the context if the water-waves system the strength of the surface tension determines the relevant model. It turned out that  well-posedness theory of KP-I and KP-II are very different : KP-II is a semi-linear equation while the KP-I equation is a quasi-linear one. However, in the case of slightly weaker dispersion in the main direction of propagation, the KP-II model becomes a quasi-linear equation when periodic transverse perturbations are considered. We will show that despite this severe difficulty we can prove global well-posedness in L^2 of some weakly dispersive KP-II models. We crucially rely on recent advances in the decoupling theory and on a new implementation of the short-time Fourier restriction method. This is a joint work with Sebastian Herr and Robert Schippa.