相互作用的Brinkman-Forchheimer方程组与Darcy方程组的结构稳定性

Structural Stability for the Brinkman-Forchheimer Equations Interfacing with a Darcy Equations

研究了在R^(3)中有界区域内的多孔介质中相互作用的Brinkman-Forchheimer流体与Darcy流体方程组解的结构稳定性,假设在Ω_(1)中流体速度较慢,满足BrinkmanForchheimer方程组,而在Ω_(2)中,饱和流体满足Darcy方程组.借助于温度的四阶范数估计以及Sobolev不等式,构造能量表达式,推出该表达式所满足的微分不等式,积分得到了相互作用Brinkman-Forchheimer与Darcy流体方程组的解对Brinkman系数的连续依赖性结果.

The structural stability for the Brinkman-Forchheimer fuid interfacing with a Darcy fuid in a bounded region in R^(3) was studied.We assumed that the velocity of fluid was slow and it was governed by the Brinkman-Forchheimer equations in Ω_(1),while in Ω_(2),we supposed that the saturated fow satisfies the Darcy equations.With the aid of the fourth norm estimates for the temperatures and the Sobolev inequality,we formulated an energy expression,and the expression satisfies a differential inequality.By integrating,we were able to demonstrate the continuous dependence result for the Brinkman coefficient.