Almost sure global nonlinear smoothing for the 2D NLS
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917146846560256 |
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| author | Sun, Chenmin Tzvetkov, Nikolay |
| author_facet | Sun, Chenmin Tzvetkov, Nikolay |
| contents | 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 Erdoğan--Tzirakis, which remains unknown on multidimensional torus.
Our argument is based on a quantitative quasi-invariance of Gaussian measures with covariance operator $(1-Δ)^{-s}$ for $s>2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almost sure global nonlinear smoothing for the 2D NLS Sun, Chenmin Tzvetkov, Nikolay Analysis of PDEs Probability 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 Erdoğan--Tzirakis, which remains unknown on multidimensional torus. Our argument is based on a quantitative quasi-invariance of Gaussian measures with covariance operator $(1-Δ)^{-s}$ for $s>2$. |
| title | Almost sure global nonlinear smoothing for the 2D NLS |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2512.13088 |