The structural stability of the Boussinesq fluid interfacing with a Darcy fluid in a bounded region in $R^2$ was studied. We assumed that the viscous fluid was governed by the Boussinesq equations in ${\Omega }_1$, while in ${\Omega }_2$, we supposed that the flow satisfies the Darcy equations. Some interfacing boundary conditions are imposed. The traditional $\mathit{Poin}\mathit{car}\acute{e}$ inequalities can’t be used. With the aid of some useful a priori bounds and some new $\mathit{Poin}\mathit{car}\acute{e}$ inequalities, we were able to demonstrate the continuous dependence result on the interface coefficient $\alpha$. The result showed that the structural stability is valid for the interfacing problem.

中文翻译：

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Boussinesq 流体在有界区域中与 Darcy 流体界面的结构稳定性 ${\mathrm{电阻}}^2$

Boussinesq 流体在有界区域中与 Darcy 流体界面的结构稳定性 ${\mathrm{电阻}}^2$被研究了。我们假设粘性流体是由 Boussinesq 方程控制的${\Omega }_1$， 而在 ${\Omega }_2$，我们假设流动满足达西方程。强加了一些接口边界条件。传统的$\mathit{点}\mathit{车}\acute{\mathrm{电子}}$不能使用不等式。借助一些有用的先验界限和一些新的$\mathit{点}\mathit{车}\acute{\mathrm{电子}}$ 不等式，我们能够证明对界面系数的连续依赖结果 $\alpha$. 结果表明，结构稳定性对于界面问题是有效的。