Global strong solution for the stochastic tamed Chemotaxis-Navier-Stokes system in $\mathbb{R}^3$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918062600486912 |
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| author | Xu, Fan Zhang, Lei Liu, Bin |
| author_facet | Xu, Fan Zhang, Lei Liu, Bin |
| contents | In this work, we consider the 3D Cauchy problem for a coupled system arising in biomathematics, consisting of a chemotaxis model with a cubic logistic source and the stochastic tamed Navier-Stokes equations (STCNS, for short). Our main goal is to establish the existence and uniqueness of a global strong solution (strong in both the probabilistic and PDE senses) for the 3D STCNS system with large initial data. To achieve this, we first introduce a triple approximation scheme by using the Friedrichs mollifier, frequency truncation operators, and cut-off functions. This scheme enables the construction of sufficiently smooth approximate solutions and facilitates the effective application of the entropy-energy method. Then, based on a newly derived stochastic version of the entropy-energy inequality, we further establish some a priori higher-order energy estimates, which together with the stochastic compactness method, allow us to construct the strong solution for the STCNS system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17059 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global strong solution for the stochastic tamed Chemotaxis-Navier-Stokes system in $\mathbb{R}^3$ Xu, Fan Zhang, Lei Liu, Bin Analysis of PDEs Probability In this work, we consider the 3D Cauchy problem for a coupled system arising in biomathematics, consisting of a chemotaxis model with a cubic logistic source and the stochastic tamed Navier-Stokes equations (STCNS, for short). Our main goal is to establish the existence and uniqueness of a global strong solution (strong in both the probabilistic and PDE senses) for the 3D STCNS system with large initial data. To achieve this, we first introduce a triple approximation scheme by using the Friedrichs mollifier, frequency truncation operators, and cut-off functions. This scheme enables the construction of sufficiently smooth approximate solutions and facilitates the effective application of the entropy-energy method. Then, based on a newly derived stochastic version of the entropy-energy inequality, we further establish some a priori higher-order energy estimates, which together with the stochastic compactness method, allow us to construct the strong solution for the STCNS system. |
| title | Global strong solution for the stochastic tamed Chemotaxis-Navier-Stokes system in $\mathbb{R}^3$ |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2410.17059 |