Global well-posedness of the energy-critical stochastic nonlinear wave equations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911967076155392 |
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| author | Brun, Enguerrand Li, Guopeng Liu, Ruoyuan |
| author_facet | Brun, Enguerrand Li, Guopeng Liu, Ruoyuan |
| contents | 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 Bényi-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14946 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the energy-critical stochastic nonlinear wave equations Brun, Enguerrand Li, Guopeng Liu, Ruoyuan Analysis of PDEs Probability 35L71, 35R60, 60H15 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 Bényi-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. |
| title | Global well-posedness of the energy-critical stochastic nonlinear wave equations |
| topic | Analysis of PDEs Probability 35L71, 35R60, 60H15 |
| url | https://arxiv.org/abs/2309.14946 |