The stochastic Navier-Stokes equations with general $L^{3}$ data
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908306551865344 |
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| author | Aydın, Mustafa Sencer Kukavica, Igor Xu, Fanhui |
| author_facet | Aydın, Mustafa Sencer Kukavica, Igor Xu, Fanhui |
| contents | We consider the stochastic Navier-Stokes equations with multiplicative noise with critical initial data. Assuming that the initial data $u_0$ belongs to the critical space $L^{3}$ almost surely, we construct a unique local-in-time probabilistically strong solution. We also prove an analogous result for data in the critical space~$H^\frac{1}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The stochastic Navier-Stokes equations with general $L^{3}$ data Aydın, Mustafa Sencer Kukavica, Igor Xu, Fanhui Probability Analysis of PDEs We consider the stochastic Navier-Stokes equations with multiplicative noise with critical initial data. Assuming that the initial data $u_0$ belongs to the critical space $L^{3}$ almost surely, we construct a unique local-in-time probabilistically strong solution. We also prove an analogous result for data in the critical space~$H^\frac{1}{2}$. |
| title | The stochastic Navier-Stokes equations with general $L^{3}$ data |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2504.05648 |