论文标题
达西定律的急剧收敛率
Sharp Convergence Rates for Darcy's Law
论文作者
论文摘要
本文涉及达西定律，该定律是在多孔介质中流动的不可压缩粘性液。我们在$ d \ ge 2 $的$ r^d $中定期穿孔和有限的域中建立了尖锐的$ o（\ sqrt {\ e}）$收敛率，其中$ \ e $代表坚固的障碍物的大小。这是通过构造两个边界校正器来控制由不可压缩性条件产生的边界层以及在其渐近扩展中解决方案和领先术语之间边界值的差异来实现的。其中一个校正器处理切向边界数据，而另一个校正器处理正常的边界数据。
This paper is concerned with Darcy's law for an incompressible viscous fluid flowing in a porous medium. We establish the sharp $O(\sqrt{\e})$ convergence rate in a periodically perforated and bounded domain in $R^d$ for $d\ge 2$, where $\e$ represents the size of solid obstacles. This is achieved by constructing two boundary correctors to control the boundary layers created by the incompressibility condition and the discrepancy of boundary values between the solution and the leading term in its asymptotic expansion. One of the correctors deals with the tangential boundary data, while the other handles the normal boundary data.
