A chemotaxis-fluid model driven by Lévy noise in $\mathbb{R}^2$
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916353068236800 |
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| author | Xu, Fan Zhang, Lei Liu, Bin |
| author_facet | Xu, Fan Zhang, Lei Liu, Bin |
| contents | In this paper, we investigate the existence and uniqueness of global solutions to the Cauchy problem for a coupled stochastic chemotaxis-Navier-Stokes system with multiplicative Lévy noises in $\mathbb{R}^2$. The existence of global martingale solutions is proved under a framework that is based on the Faedo-Galerkin approximation scheme and stochastic compactness method, where the verification of tightness depends crucially on a novel stochastic version of Lyapunov functional inequality and proper compactness criteria in Fréchet spaces. A pathwise uniqueness result is also established with suitable assumption on the jump noises, which indicates that the considered system admits a unique global strong solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05685 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A chemotaxis-fluid model driven by Lévy noise in $\mathbb{R}^2$ Xu, Fan Zhang, Lei Liu, Bin Analysis of PDEs Probability In this paper, we investigate the existence and uniqueness of global solutions to the Cauchy problem for a coupled stochastic chemotaxis-Navier-Stokes system with multiplicative Lévy noises in $\mathbb{R}^2$. The existence of global martingale solutions is proved under a framework that is based on the Faedo-Galerkin approximation scheme and stochastic compactness method, where the verification of tightness depends crucially on a novel stochastic version of Lyapunov functional inequality and proper compactness criteria in Fréchet spaces. A pathwise uniqueness result is also established with suitable assumption on the jump noises, which indicates that the considered system admits a unique global strong solution. |
| title | A chemotaxis-fluid model driven by Lévy noise in $\mathbb{R}^2$ |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2408.05685 |