Almost global existence for the stochastic Navier-Stokes equations with small $H^{1/2}$ data
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909459136118784 |
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| author | Aydın, Mustafa Sencer Kukavica, Igor Xu, Fanhui |
| author_facet | Aydın, Mustafa Sencer Kukavica, Igor Xu, Fanhui |
| contents | We address the global existence of solutions to the stochastic Navier-Stokes equations with multiplicative noise and with initial data in $H^{1/2}(\mathbb{T}^{3})$. We prove that the solution exists globally in time with probability arbitrarily close to~$1$ if the initial data and noise are sufficiently small. If the noise is not assumed to be small, then the solution is global on a sufficiently small deterministic time interval with probability arbitrarily close to~$1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10331 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almost global existence for the stochastic Navier-Stokes equations with small $H^{1/2}$ data Aydın, Mustafa Sencer Kukavica, Igor Xu, Fanhui Probability Analysis of PDEs We address the global existence of solutions to the stochastic Navier-Stokes equations with multiplicative noise and with initial data in $H^{1/2}(\mathbb{T}^{3})$. We prove that the solution exists globally in time with probability arbitrarily close to~$1$ if the initial data and noise are sufficiently small. If the noise is not assumed to be small, then the solution is global on a sufficiently small deterministic time interval with probability arbitrarily close to~$1$. |
| title | Almost global existence for the stochastic Navier-Stokes equations with small $H^{1/2}$ data |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2501.10331 |