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Nicolas Camps: Towards the invariance of the Gibbs measure for NLS on the sphere

Time: Wed 2023-10-04 09.30 - 10.30

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Nicolas Camps, Université de Nantes

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This talk is devoted to a statistical approach to nonlinear waves on surfaces. Specifically, we consider the cubic Schrödinger equation on the 2 dimensional sphere and we study the collective behavior of solutions on the support of the Gibbs measure. We first evidence strong instabilities due to concentrated spherical harmonics around a great circle, which make the Cauchy problem very challenging. Then, we present a probabilistic quasi-linear resolution scheme to prove long time existence of solutions on the support of the Gibbs measure.

This is ongoing joint work with Nicolas Burq, Chenmin Sun and Nikolay Tzvetkov.