TY - JOUR
T1 - Averaging of a Three-Dimensional Brinkman-Forchheimer Equation with Singularly Oscillating Forces
AU - Song , Xueli
AU - Li , Xiaofeng
AU - Deng , Xi
AU - Qiao , Biaoming
JO - Journal of Partial Differential Equations
VL - 4
SP - 355
EP - 376
PY - 2024
DA - 2024/12
SN - 37
DO - http://doi.org/10.4208/jpde.v37.n4.1
UR - https://global-sci.org/intro/article_detail/jpde/23686.html
KW - Brinkman-Forchheimer equation, uniform attractor, singularly oscillating external force, uniform boundedness.
AB - <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>