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arXiv · 2512.13088

Almost sure global nonlinear smoothing for the 2D NLS

Chenmin Sun·Nikolay Tzvetkov
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Abstract

In this article, we prove an almost-sure global in time nonlinear smoothing effect for NLS on the two-dimensional torus. For deterministic data, this phenomenon was proved for the NLS on the circle by Erdo\u{g}an--Tzirakis, which remains unknown on multidimensional torus. Our argument is based on a quantitative quasi-invariance of Gaussian measures with covariance operator $(1-\Delta)^{-s}$ for $s>2$.

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Chenmin Sun, Nikolay Tzvetkov. 2025-12-15. Almost sure global nonlinear smoothing for the 2D NLS. https://arxiv.org/abs/2512.13088

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