粗糙度双重效应下雷诺近似的收敛性
Convergence to the Reynolds approximation with a double effect of roughness
摘要：
我们证明了润滑近似扰动的边界的非规则粗糙度。我们将展示如何使用足够的粗糙度配置文件的底部的流动可能会加速。我们明确的轮廓中的一些突然的变化可能产生的影响。极限系统在数学上是合理的，通过一个变种的概念，两个规模的收敛。最后，我们提出了一些数值结果，说明在三维情况下的极限系统。
英文摘要：
We prove that the lubrication approximation is perturbed by a non-regular roughness of the boundary. We show how the flow may be accelerated using adequate rugosity profiles on the bottom. We explicit the possible effects of some abrupt changes in the profile. The limit system is mathematically justified through a variant of the notion of two-scale convergence. Finally, we present some numerical results, illustrating the limit system in the three-dimensional case.
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