Smooth attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities
✍ Scribed by Kalantarov, Varga; Zelik, Sergey
- Book ID
- 126493939
- Publisher
- American Institute of Mathematical Sciences
- Year
- 2012
- Tongue
- English
- Weight
- 456 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1534-0392
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## Abstract In this paper, we investigate the asymptotic behavior of solutions of the three‐dimensional Brinkman–Forchheimer equation. We first prove the existence and uniqueness of solutions of the equation in __L__^2^, and then show that the equation has a global attractor in __H__^2^ when the ex
In this article, the existence of a global attractor for the Brinkman-Forchheimer equations in the phase space H 1 0 (Ω ) is proved.
This study focuses on the Brinkman-Forchheimer equation u t = γ uau -b|u|u -c|u| β u -∇ p + f in an open, bounded domain Ω and the existence of a global attractor in the phase space H 1 0 (Ω ) is established.