Regularization by noise for the energy- and mass-critical nonlinear Schrödinger equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909604987797504 |
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| author | Spitz, Martin Zhang, Deng Zhao, Zhenqi |
| author_facet | Spitz, Martin Zhang, Deng Zhao, Zhenqi |
| contents | In this article we prove a regularization by noise phenomenon for the energy-critical and mass-critical nonlinear Schrödinger equations. We show that for any deterministic data, the probability that the corresponding solution exists globally and scatters goes to one as the strength of the non-conservative noise goes to infinity. The proof relies on the rescaling transform and a new observation on the rapid uniform decay of geometric Brownian motions after short time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05421 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularization by noise for the energy- and mass-critical nonlinear Schrödinger equations Spitz, Martin Zhang, Deng Zhao, Zhenqi Analysis of PDEs Probability In this article we prove a regularization by noise phenomenon for the energy-critical and mass-critical nonlinear Schrödinger equations. We show that for any deterministic data, the probability that the corresponding solution exists globally and scatters goes to one as the strength of the non-conservative noise goes to infinity. The proof relies on the rescaling transform and a new observation on the rapid uniform decay of geometric Brownian motions after short time. |
| title | Regularization by noise for the energy- and mass-critical nonlinear Schrödinger equations |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2505.05421 |