@Article{JPDE-37-355,
author = {Song , XueliLi , XiaofengDeng , Xi and Qiao , Biaoming},
title = {Averaging of a Three-Dimensional Brinkman-Forchheimer Equation with Singularly Oscillating Forces},
journal = {Journal of Partial Differential Equations},
year = {2024},
volume = {37},
number = {4},
pages = {355--376},
abstract = {<p style="text-align: justify;">We consider the uniform attractors of a 3D non-autonomous Brinkman–
Forchheimer equation with a singularly oscillating force $$\frac{\partial u}{\partial t}-\gamma\Delta u+au+b|u|u+c|u|^2u+\nabla p=f_0(x,t)+\varepsilon^{-\rho}f_1\Bigg(x,\frac{t}{\varepsilon}\Bigg),$$ for $ρ∈[0,1)$ and $\varepsilon&gt;0,$ and the averaged equation (corresponding to the limiting case $\varepsilon=0$) $$\frac{\partial u}{\partial t}-\gamma\Delta u+au+b|u|u+c|u|^2u+\nabla p=f_0(x,t).$$Given a certain translational compactness assumption for the external forces, we obtain
the uniform boundedness of the uniform attractor $\mathcal{A}^{\varepsilon}$ of the first system in $(H^1_0(Ω))^3,$ and prove that when $\varepsilon$ tends to 0, the uniform attractor of the first system $\mathcal{A}^{\varepsilon}$ converges
to the attractor $\mathcal{A}^0$ of the second system.&nbsp;</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v37.n4.1},
url = {http://global-sci.org/intro/article_detail/jpde/23686.html}
}