Strong well-posedness of the two-dimensional stochastic Navier-Stokes equation on moving domains
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908372681359360 |
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| author | Chen, Ping Pan, Tianyi Zhang, Tusheng |
| author_facet | Chen, Ping Pan, Tianyi Zhang, Tusheng |
| contents | In this paper, we establish the strong($H^1$) well-posedness of the two dimensional stochastic Navier-Stokes equation with multiplicative noise on moving domains. Due to the nonlocality effect, this equation exhibits a ``piecewise" variational setting. Namely the global well-posedness of this equation is decomposed into the well-posedness of a family of stochastic partial differential equations(SPDEs) in the variational setting on each small time-interval. We first examine the well-posedness on each time interval, which does not have (nonhomogeneous) coercivity. Subsequently, we give an estimate of lower bound of length of the time-interval, which enables us to achieve the global well-posedness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong well-posedness of the two-dimensional stochastic Navier-Stokes equation on moving domains Chen, Ping Pan, Tianyi Zhang, Tusheng Probability Analysis of PDEs 35R37, 60H15 In this paper, we establish the strong($H^1$) well-posedness of the two dimensional stochastic Navier-Stokes equation with multiplicative noise on moving domains. Due to the nonlocality effect, this equation exhibits a ``piecewise" variational setting. Namely the global well-posedness of this equation is decomposed into the well-posedness of a family of stochastic partial differential equations(SPDEs) in the variational setting on each small time-interval. We first examine the well-posedness on each time interval, which does not have (nonhomogeneous) coercivity. Subsequently, we give an estimate of lower bound of length of the time-interval, which enables us to achieve the global well-posedness. |
| title | Strong well-posedness of the two-dimensional stochastic Navier-Stokes equation on moving domains |
| topic | Probability Analysis of PDEs 35R37, 60H15 |
| url | https://arxiv.org/abs/2504.13468 |