Journals
Resources
About Us
Open Access

Averaging of a Three-Dimensional Brinkman-Forchheimer Equation with Singularly Oscillating Forces

Averaging of a Three-Dimensional Brinkman-Forchheimer Equation with Singularly Oscillating Forces

Year:    2024

Author:    Xueli Song, Xiaofeng Li, Xi Deng, Biaoming Qiao

Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 4 : pp. 355–376

Abstract

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 $\varepsilon>0,$ 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. 

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v37.n4.1

Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 4 : pp. 355–376

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Brinkman-Forchheimer equation uniform attractor singularly oscillating external force uniform boundedness.

Author Details

Xueli Song

Xiaofeng Li

Xi Deng

Biaoming Qiao