有界区域内Forchheimer流体对接Darcy流体的连续依赖性

Continuous Dependence for the Forchheimer Fluid Interfacing with a Darcy Fluidin a Bounded Domain

研究Forchheimer系数b在有界区域内,关于粘性流体对接的多孔介质的连续依赖性。假设在1?中,粘性流体是缓慢流动的,所控制的方程是Forchheimer方程;在2?的多孔介质中,我们假设流体所控制的方程是Darcy方程。首先进行先验假设得到关于u和v的L2范数的界的估计;然后利用杨氏不等式,散度定理还有其他的微分不等式,经过一定的放缩,构造出恰当的辅助函数;最后我们利用Gronwall不等式处理辅助函数,得到解关于Forchheimer系数b的连续依赖性。

This paper researches the continuous dependence of the Forchheimer coefficient b in a bounded domain of a viscous fluid interfacing with a porous media. We assume that the fluid is slow and the governing equations are Forchheimer equations. While for the porous media, we suppose that the fluid is Darcy equations. First, we can get the bound of estimate about the L2 norm of u and v by priori estimate. Then we use the Young inequality, divergence theorem and other differential inequalities to construct proper auxiliary function after an appropriate estimate. In the end, using Gronwall inequality to deal with the auxiliary function, we can get the continuous dependence of solution about the Forchheimer coefficient b.