## Topological Methods in Nonlinear Analysis

### The trajectory attractor and its limiting behavior for the convective Brinkman-Forchheimer equations

#### Abstract

This paper studies the trajectory behavior of the convective Brinkman-Forchheimer equations in three-dimensional (3D) bounded domains. We first prove the existence of the trajectory attractor ${\mathcal A}^{\rm tr}_\alpha$ for the natural translation semigroup in the trajectory space. Then we establish that the trajectory attractor $\mathcal{A}^{\rm tr}_\alpha$ converges, as $\alpha\rightarrow 0^+$, to the trajectory attractor $\mathcal{A}^{\rm tr}_0$ of the 3D Navier-Stokes equations in a proper topological space.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 44, Number 2 (2014), 413-433.

Dates
First available in Project Euclid: 11 April 2016

https://projecteuclid.org/euclid.tmna/1460381363

Mathematical Reviews number (MathSciNet)
MR3328349

Zentralblatt MATH identifier
1362.35056

#### Citation

Zhao, Caidi; Kong, Lei; Liu, Guowei; Zhao, Min. The trajectory attractor and its limiting behavior for the convective Brinkman-Forchheimer equations. Topol. Methods Nonlinear Anal. 44 (2014), no. 2, 413--433. https://projecteuclid.org/euclid.tmna/1460381363

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