A priori bounds were derived for the flow in a bounded domain for the viscous-porous interfacing fluids. We assumed that the viscous fluid was slow in $\Omega _{1}$ , which was governed by the Boussinesq equations. For a porous medium in $\Omega _{2}$ , we supposed that the flow satisfied the Darcy equations. With the aid of these a priori bounds we were able to demonstrate the result of the continuous dependence type for the Boussinesq coefficient λ. Following the method of a first-order differential inequality, we can further obtain the result that the solution depends continuously on the interface boundary coefficient α. These results showed that the structural stability is valid for the interfacing problem.

中文翻译：

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有界域中与Darcy方程对接的Boussinesq方程的结构稳定性

在粘性-多孔界面流体的有界域中为流动导出了先验界。我们假设粘性流体在\\ Omega _ {1} $中缓慢，这由Boussinesq方程控制。对于$ Omega _ {2} $中的多孔介质，我们认为该流量满足Darcy方程。借助这些先验边界，我们能够证明Boussinesq系数λ的连续依赖类型的结果。遵循一阶微分不等式的方法，我们可以进一步得出结果，该解连续依赖于界面边界系数α。这些结果表明，结构稳定性对于界面问题是有效的。