1. Asymptotic analysis of the 2D and 3D convective Brinkman–Forchheimer equations in unbounded domains.
- Author
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Kinra, Kush and Mohan, Manil T.
- Subjects
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FRACTAL dimensions , *INCOMPRESSIBLE flow , *FLUID flow , *POROUS materials , *NEIGHBORHOODS , *CONVECTIVE flow - Abstract
In this work, we carry out the asymptotic analysis of two- and three-dimensional convective Brinkman–Forchheimer (CBF) equations, which characterize the motion of incompressible fluid flows in a saturated porous medium. We establish the existence of a global attractor in both bounded (using compact embedding) and unbounded Poincaré domains (using asymptotic compactness property). In Poincaré domains, the estimates for Hausdorff as well as fractal dimensions of the global attractors are also obtained. We then show an upper semicontinuity of global attractors with respect to domains for CBF equations. We consider an expanding sequence of simply connected, bounded and smooth subdomains Ωm of the Poincaré domain Ω such that Ωm → Ω as m →∞. If 풜m and 풜 are the global attractors of CBF equations corresponding to Ωm and Ω, respectively, then we show that for large enough m, the global attractor 풜m enters into any neighborhood 풰(풜) of 풜. The presence of the Darcy term in CBF equations helps us to obtain the above mentioned results in general unbounded domains also. Finally, we discuss the quasi-stability property of the semigroup associated with CBF equations in bounded domains and establish the existence of finite fractal dimensional global as well as exponential attractors. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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