三维全空间上Brinkman-Forchheimer方程弱解的L^2衰减性  

L^2-decay of Weak Solutions for the Three-dimensional Brinkman-Forchheimer Equations in R^3

作　　者：宋雪丽[1] 徐爽 乔宝明[1] SONG Xue-li;XU Shuang;QIAO Bao-ming(College of Science,Xi'an University of Science and Technology,Xi'an 710054,China)

机构地区：[1]西安科技大学理学院,陕西西安710054

出　　处：《数学的实践与认识》2020年第22期307-314,共8页Mathematics in Practice and Theory

基　　金：陕西省自然基金(2018JM1047,2019JM-283);国家自然科学基金(11601417)。

摘　　要：研究了如下三维Brinkman-Forchheimer方程ut-Δu+au+b|u|βu+▽p=0弱解的衰减性及解的渐近稳定性.首先使用Fourier分解方法研究了当β>7/3时弱解的L2衰减性,接下来讨论了在大初值扰动下解的渐近稳定性.In this paper,we study the L^2-decay and the asymptotic stability of the weak solutions of the following three-dimensional Brinkman-Forchheimer equations in R^3:ut- △u+au+b|u|^βu+▽p=0 Firstly,we use the Fourier splitting method to study the decay of weak solutions in the L^2 space when β>7/3.Then we investigate the asymp totic st ability of the solutions to the system under large initial perturbation.

关 键 词：Brinkman—Forchheimer方程 L^2衰减 渐近稳定性 

分 类 号：O175[理学—数学]