On existence of local and global strong solutions for the stochastic tamed Navier-Stokes equations on $\mathbb{R}^3$
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| Format: | Preprint |
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2026
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| _version_ | 1866913178636517376 |
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| author | Podder, Bikram Kumar, Surendra |
| author_facet | Podder, Bikram Kumar, Surendra |
| contents | We study the existence of local and global strong solutions for the stochastic tamed Navier--Stokes equations on the whole space $\mathbb{R}^3$, driven by multiplicative Wiener noise and compensated Lévy jump noise. For $p > 3$, we first prove the existence of a pathwise unique maximal local $L^p$-strong solution for divergence-free, $\mathcal{F}_0$-measurable initial data in $L^p(Ω; L^p(\mathbb{R}^3;\mathbb{R}^3))$. For initial data additionally belonging to $L^2(Ω; H^1(\mathbb{R}^3;\mathbb{R}^3))$, we overcome the non-local pressure obstruction inherent to the whole space, to establish the existence of a pathwise unique global strong solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_03734 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On existence of local and global strong solutions for the stochastic tamed Navier-Stokes equations on $\mathbb{R}^3$ Podder, Bikram Kumar, Surendra Analysis of PDEs Probability 60H15, 35R60, 35Q30, 76D05 We study the existence of local and global strong solutions for the stochastic tamed Navier--Stokes equations on the whole space $\mathbb{R}^3$, driven by multiplicative Wiener noise and compensated Lévy jump noise. For $p > 3$, we first prove the existence of a pathwise unique maximal local $L^p$-strong solution for divergence-free, $\mathcal{F}_0$-measurable initial data in $L^p(Ω; L^p(\mathbb{R}^3;\mathbb{R}^3))$. For initial data additionally belonging to $L^2(Ω; H^1(\mathbb{R}^3;\mathbb{R}^3))$, we overcome the non-local pressure obstruction inherent to the whole space, to establish the existence of a pathwise unique global strong solution. |
| title | On existence of local and global strong solutions for the stochastic tamed Navier-Stokes equations on $\mathbb{R}^3$ |
| topic | Analysis of PDEs Probability 60H15, 35R60, 35Q30, 76D05 |
| url | https://arxiv.org/abs/2605.03734 |