Probabilistic well-posedeness for the nonlinear Schrödinger equation on the $2d$ sphere I: positive regularities
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915356683010048 |
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| author | Burq, Nicolas Camps, Nicolas Sun, Chenmin Tzvetkov, Nikolay |
| author_facet | Burq, Nicolas Camps, Nicolas Sun, Chenmin Tzvetkov, Nikolay |
| contents | We establish the probabilistic well-posedness of the nonlinear Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic well-posedeness for the nonlinear Schrödinger equation on the $2d$ sphere I: positive regularities Burq, Nicolas Camps, Nicolas Sun, Chenmin Tzvetkov, Nikolay Analysis of PDEs 35Q55, 35A01, 35R01, 35R60, 37KXX We establish the probabilistic well-posedness of the nonlinear Schrödinger 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. |
| title | Probabilistic well-posedeness for the nonlinear Schrödinger equation on the $2d$ sphere I: positive regularities |
| topic | Analysis of PDEs 35Q55, 35A01, 35R01, 35R60, 37KXX |
| url | https://arxiv.org/abs/2404.18229 |