论文标题
Stokes/Cahn-Hilliard系统的尖锐界面限制，第二部分：近似解决方案
Sharp Interface Limit of a Stokes/Cahn-Hilliard System, Part II: Approximate Solutions
论文作者
论文摘要
我们通过使用匹配的渐近物扩展方法来为Stokes/Cahn-Hilliard系统构建严格的合适近似解决方案。这是在此贡献的第一部分中给出的融合证明的主要步骤，其中显示了在二维，有界和光滑的域中耦合Stokes/cahn-Hilliard系统的严格尖锐界面极限。作为与早期作品相比的新颖性，我们引入了分数订单项，这一点很重要，但是有问题的特征，即在任意强大的规范中可能不会以$ε$统一的估计。结果，在考虑Stokes/cahn-Hilliard系统中的近似值时，获得了必要的估计。
We construct rigorously suitable approximate solutions to the Stokes/Cahn-Hilliard system by using the method of matched asymptotics expansions. This is a main step in the proof of convergence given in the first part of this contribution, where the rigorous sharp interface limit of a coupled Stokes/Cahn-Hilliard system in a two dimensional, bounded and smooth domain is shown. As a novelty compared to earlier works, we introduce fractional order terms, which are of significant importance, but share the problematic feature that they may not be uniformly estimated in $ε$ in arbitrarily strong norms. As a consequence, gaining necessary estimates for the error, which occurs when considering the approximations in the Stokes/Cahn-Hilliard system, is rather involved.
