Global well-posedness of the energy-critical stochastic nonlinear wave equations
| Autor: | Brun, Enguerrand, Li, Guopeng, Liu, Ruoyuan |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | J. Differential Equations 397 (2024), 316-348 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jde.2024.03.032 |
| Popis: | We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on $\mathbb{R}^{d}$ and $\mathbb{T}^{d}$ with $d \geq 3$. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by B\'enyi-Oh-Pocovnicu (2015) and Pocovnicu (2017) and in the context of stochastic PDEs by Oh-Okamoto (2020), we prove global well-posedness of the defocusing energy-critical SNLW. In particular, on $\mathbb{T}^d$, we prove global well-posedness with the stochastic forcing below the energy space. Comment: 26 pages |
| Databáze: | arXiv |
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