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arXiv · 2404.18229

Probabilistic well-posedeness for the nonlinear Schr\"odinger equation on the $2d$ sphere I: positive regularities

Nicolas Burq·Nicolas Camps·Chenmin Sun·Nikolay Tzvetkov
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Abstract

We establish the probabilistic well-posedness of the nonlinear Schr\"odinger equation on the $2d$ sphere $\mathbb{S}^{2}$. The initial data are distributed according to Gaussian measures with typical regularity $H^{s}(\mathbb{S}^{2})$, for $s>0$. This level of regularity goes significantly beyond existing deterministic results, in a regime where the flow map cannot be extended uniformly continuously.

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Nicolas Burq, Nicolas Camps, Chenmin Sun, Nikolay Tzvetkov. 2024-04-28. Probabilistic well-posedeness for the nonlinear Schr\"odinger equation on the $2d$ sphere I: positive regularities. https://arxiv.org/abs/2404.18229

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