Speaker: Prof. Nikolay Tzvetkov ，ENS Lyon

Inviter: 范晨捷副研究员

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

Language: English

Time & Venue: 2025.05.21 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.