Stochastic complex Ginzburg-Landau equation on compact surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909517209403392 |
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| author | Robert, Tristan Zine, Younes |
| author_facet | Robert, Tristan Zine, Younes |
| contents | We study a stochastic complex Ginzburg-Landau equation (SCGL) on compact surfaces with magnetic Laplacian and polynomial nonlinearity, forced by a space-time white noise. After renormalizing the equation in a suitable manner, we show that the dynamics is locally well-posed. Moreover, we prove deterministic global well-posedness for the defocusing SCGL in the weakly dispersive regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21128 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic complex Ginzburg-Landau equation on compact surfaces Robert, Tristan Zine, Younes Analysis of PDEs Probability 35K15, 60H15, 58J35 We study a stochastic complex Ginzburg-Landau equation (SCGL) on compact surfaces with magnetic Laplacian and polynomial nonlinearity, forced by a space-time white noise. After renormalizing the equation in a suitable manner, we show that the dynamics is locally well-posed. Moreover, we prove deterministic global well-posedness for the defocusing SCGL in the weakly dispersive regime. |
| title | Stochastic complex Ginzburg-Landau equation on compact surfaces |
| topic | Analysis of PDEs Probability 35K15, 60H15, 58J35 |
| url | https://arxiv.org/abs/2502.21128 |