Pullback $V$-Attractors of the Stochastic Calmed 3$D$ Navier-Stokes Equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914061398048768 |
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| author | Duan, Yawen Gu, Anhui |
| author_facet | Duan, Yawen Gu, Anhui |
| contents | In this paper, we investigate a calmed version of the 3$D$ rotational Navier-Stokes equations driven by additive noise. First, we use the Ornstein-Uhlenbeck process to transform the equation into a random one. By using the Galerkin approximation, we establish the global well-posedness of solutions for the calmed system. Then, we demonstrate the existence of a closed, measurable $\mathcal{D}_V$-pullback absorbing set. Finally, by proving the pullback flattening property, we obtain the existence of a $\mathcal{D}_V$-pullback attractor in \(V\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23553 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pullback $V$-Attractors of the Stochastic Calmed 3$D$ Navier-Stokes Equations Duan, Yawen Gu, Anhui Analysis of PDEs 35B40, 35B41, 35Q35, 37L55, 60H15 In this paper, we investigate a calmed version of the 3$D$ rotational Navier-Stokes equations driven by additive noise. First, we use the Ornstein-Uhlenbeck process to transform the equation into a random one. By using the Galerkin approximation, we establish the global well-posedness of solutions for the calmed system. Then, we demonstrate the existence of a closed, measurable $\mathcal{D}_V$-pullback absorbing set. Finally, by proving the pullback flattening property, we obtain the existence of a $\mathcal{D}_V$-pullback attractor in \(V\). |
| title | Pullback $V$-Attractors of the Stochastic Calmed 3$D$ Navier-Stokes Equations |
| topic | Analysis of PDEs 35B40, 35B41, 35Q35, 37L55, 60H15 |
| url | https://arxiv.org/abs/2509.23553 |