Invariant measures for stochastic Burgers equation on unbounded domains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913884934242304 |
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| author | Liu, Zhenxin Shi, Zhiyuan |
| author_facet | Liu, Zhenxin Shi, Zhiyuan |
| contents | In this paper, we investigate the stochastic damped Burgers equation with multiplicative noise defined on the entire real line. We demonstrate the existence and uniqueness of a mild solution to the stochastic damped Burgers equation and establish that the solution is uniformly bounded in time. Furthermore, by employing the uniform estimates on the tails of the solution, we obtain the tightness of a family of probability distributions of the solution. Subsequently, by applying the Krylov-Bogolioubov theorem, we establish the existence of invariant measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariant measures for stochastic Burgers equation on unbounded domains Liu, Zhenxin Shi, Zhiyuan Dynamical Systems Probability 35Q35, 35R60, 60H15 In this paper, we investigate the stochastic damped Burgers equation with multiplicative noise defined on the entire real line. We demonstrate the existence and uniqueness of a mild solution to the stochastic damped Burgers equation and establish that the solution is uniformly bounded in time. Furthermore, by employing the uniform estimates on the tails of the solution, we obtain the tightness of a family of probability distributions of the solution. Subsequently, by applying the Krylov-Bogolioubov theorem, we establish the existence of invariant measures. |
| title | Invariant measures for stochastic Burgers equation on unbounded domains |
| topic | Dynamical Systems Probability 35Q35, 35R60, 60H15 |
| url | https://arxiv.org/abs/2506.07119 |