Global existence of the stochastic Navier-Stokes equations in $L^3$ with small data
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929526691332096 |
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| author | Kukavica, Igor Xu, Fanhui |
| author_facet | Kukavica, Igor Xu, Fanhui |
| contents | We address the global-in-time existence and pathwise uniqueness of solutions for the stochastic incompressible Navier-Stokes equations with a multiplicative noise on the three-dimensional torus. Under natural smallness conditions on the noise, we prove the almost global existence result for small $L^{3}$ data. Namely, we show that for data sufficiently small, there exists a global-in-time strong $L^{3}$ solution in a space of probability arbitrarily close to~$1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global existence of the stochastic Navier-Stokes equations in $L^3$ with small data Kukavica, Igor Xu, Fanhui Probability Analysis of PDEs We address the global-in-time existence and pathwise uniqueness of solutions for the stochastic incompressible Navier-Stokes equations with a multiplicative noise on the three-dimensional torus. Under natural smallness conditions on the noise, we prove the almost global existence result for small $L^{3}$ data. Namely, we show that for data sufficiently small, there exists a global-in-time strong $L^{3}$ solution in a space of probability arbitrarily close to~$1$. |
| title | Global existence of the stochastic Navier-Stokes equations in $L^3$ with small data |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2410.02919 |