论文标题
在薄光层中，均具有Navier-Slip条件的Stokes-Problem的均质化和尺寸降低
Homogenization and dimension reduction of the Stokes-problem with Navier-Slip condition in thin perforated layers
论文作者
论文摘要
我们从两个观点上研究了在内部振荡边界上在薄的穿孔层中构成的Stokes系统：1）层的尺寸还原和2）穿孔结构的均匀化。假设穿孔是周期性的，则可以通过小参数$ε> 0（$）来描述这两个方面，该参数与层的厚度以及周期性结构的大小有关。通过让$ε$倾向于零，我们证明了解决方案的序列会收敛到满足明确定义的宏观问题的极限。更确切地说，极限速度和极限压力满足了两个压力Stokes模型，可以从中得出薄层的Darcy定律。由于非标准的边界条件，达西定律中出现了一些其他术语。
We study a Stokes system posed in a thin perforated layer with a Navier-slip condition on the internal oscillating boundary from two viewpoints: 1) dimensional reduction of the layer and 2) homogenization of the perforated structure. Assuming the perforations are periodic, both aspects can be described through a small parameter $ε>0,$ which is related to the thickness of the layer as well as the size of the periodic structure. By letting $ε$ tend to zero, we prove that the sequence of solutions converges to a limit which satisfies a well-defined macroscopic problem. More precisely, the limit velocity and limit pressure satisfy a two pressure Stokes model, from which a Darcy law for thin layers can be derived. Due to non-standard boundary conditions, some additional terms appear in Darcy's law.
