September/October 2023 $\mathbb H^1$-random attractors for 2d stochastic convective Brinkman-Forchheimer equations in unbounded domains
Kush Kinra, Manil T. Mohan
Adv. Differential Equations 28(9/10): 807-884 (September/October 2023). DOI: 10.57262/ade028-0910-807

Abstract

The asymptotic behavior of solutions of twodimensional stochastic convective Brinkman-Forchheimer (2D SCBF) equations inunbounded domains is discussed in this work (for example, Poincaré domains).We first prove the existence of $\mathbb{H}^1$-random attractors for the stochastic flow generated by 2D SCBF equations (for the absorptionexponent $r\in[1,3]$) perturbed by an additive noise on Poincaré domains $\mathcal O$. Furthermore, we deduce the existence of a unique invariant measure in $\mathbb{H}^1(\mathcal O) $ for the 2D SCBF equations defined on Poincaré domains. In addition, a remark on the extension of these results to generalunbounded domains is also provided. Finally, for 2D SCBF equations forced byadditive one-dimensional Wiener noise, we prove the upper semicontinuity ofthe random attractors, when the domain changes from bounded to unbounded (Poincaré) domain.

Citation

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Kush Kinra. Manil T. Mohan. "$\mathbb H^1$-random attractors for 2d stochastic convective Brinkman-Forchheimer equations in unbounded domains." Adv. Differential Equations 28 (9/10) 807 - 884, September/October 2023. https://doi.org/10.57262/ade028-0910-807

Information

Published: September/October 2023
First available in Project Euclid: 25 May 2023

Digital Object Identifier: 10.57262/ade028-0910-807

Subjects:
Primary: 35B41 , 35Q35 , 35R60 , 37L55 , 37N10

Rights: Copyright © 2023 Khayyam Publishing, Inc.

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Vol.28 • No. 9/10 • September/October 2023
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