Probabilistic Cauchy theory for NLS on the sphere

par Chenmin Sun (LAMA - Université Paris-Est Créteil)

lundi 17 nov. 2025, 14:00 → 15:00 Europe/Paris

Amphi Schwartz

In this talk, I will present some recent progress on the resolution of the cubic NLS on the sphere with random initial data. Our motivation is to construct the dynamics on the support of the Gibbs measure, as well as the construction of solutions in the (deterministic) super-critical regime. For NLS on S^2, we show that the Cauchy problem is globally well-posed (in a suitable sense) with the initial data distributed according to the law of the Gibbs measure. For NLS on S^3 or B^3, we can solve the cubic NLS under the radial symmetry, but with regularity strictly below the typical regularity of radial functions sampled from the Gibbs measure. In particular, our three-dimensional result improves the result of Bourgain-Bulut for the same problem. This talk is based on a series joint works with Nicolas Burq, Nicolas Camps and Nikolay Tzvetkov.