Existence and asymptotic autonomous robustness of random attractors for three-dimensional stochastic globally modified Navier-Stokes equations on unbounded domains
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915797156233216 |
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| author | My, Bui Kim Hang, Ho Thi Kinra, Kush Mohan, Manil T. Nguyen, Pham Tri |
| author_facet | My, Bui Kim Hang, Ho Thi Kinra, Kush Mohan, Manil T. Nguyen, Pham Tri |
| contents | In this article, we discuss the existence and asymptotically autonomous robustness (AAR) (almost surely) of random attractors for 3D stochastic globally modified Navier-Stokes equations (SGMNSE) on Poincaré domains (which may be bounded or unbounded). Our aim is to investigate the existence and AAR of random attractors for 3D SGMNSE when the time-dependent forcing converges to a time-independent function under the perturbation of linear multiplicative noise as well as additive noise. The main approach is to provide a way to justify that, on some uniformly tempered universe, the usual pullback asymptotic compactness of the solution operators is uniform across an infinite time-interval $(-\infty,τ]$. The backward uniform ``tail-smallness'' and ``flattening-property'' of the solutions over $(-\infty,τ]$ have been demonstrated to achieve this goal. To the best of our knowledge, this is the first attempt to establish the existence as well as AAR of random attractors for 3D SGMNSE on unbounded domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and asymptotic autonomous robustness of random attractors for three-dimensional stochastic globally modified Navier-Stokes equations on unbounded domains My, Bui Kim Hang, Ho Thi Kinra, Kush Mohan, Manil T. Nguyen, Pham Tri Probability Analysis of PDEs 37L55, 76D05, 35B41, 37B55, 35B40 In this article, we discuss the existence and asymptotically autonomous robustness (AAR) (almost surely) of random attractors for 3D stochastic globally modified Navier-Stokes equations (SGMNSE) on Poincaré domains (which may be bounded or unbounded). Our aim is to investigate the existence and AAR of random attractors for 3D SGMNSE when the time-dependent forcing converges to a time-independent function under the perturbation of linear multiplicative noise as well as additive noise. The main approach is to provide a way to justify that, on some uniformly tempered universe, the usual pullback asymptotic compactness of the solution operators is uniform across an infinite time-interval $(-\infty,τ]$. The backward uniform ``tail-smallness'' and ``flattening-property'' of the solutions over $(-\infty,τ]$ have been demonstrated to achieve this goal. To the best of our knowledge, this is the first attempt to establish the existence as well as AAR of random attractors for 3D SGMNSE on unbounded domains. |
| title | Existence and asymptotic autonomous robustness of random attractors for three-dimensional stochastic globally modified Navier-Stokes equations on unbounded domains |
| topic | Probability Analysis of PDEs 37L55, 76D05, 35B41, 37B55, 35B40 |
| url | https://arxiv.org/abs/2406.07460 |