Sharp Interface Limit for a Navier-Stokes/Allen-Cahn System with Different Viscosities
Sharp Interface Limit for a Navier-Stokes/Allen-Cahn System with Different Viscosities
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不同粘度的纳维-斯托克斯/艾伦-卡恩系统的夏普界面极限
DOI：
10.1137/22m1523698
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Mingwen Fei
中科院分区：
文献类型：
--
作者：
H. Abels;Mingwen Fei
讨论了二维有界光滑区域中耦合Navier-Stokes/Allen-Cahn系统的锐界面极限，当与扩散界面厚度成正比的参数$\vareps>0$严格趋于零时.我们证明了收敛的Navier-Stokes/Allen-Cahn系统的解决方案的解决方案的尖锐的接口模型，其中的接口的演变是由平均曲率流与一个额外的对流项耦合到一个两相Navier-Stokes系统与表面张力。这是通过构造一个近似的解决方案，从极限系统通过匹配的渐近展开与一个新的Ancillary最高阶项，然后估计其差异与真实的解决方案的援助下，一个细化的谱估计的线性化Allen-Cahn算子附近的近似解。
We discuss the sharp interface limit of a coupled Navier-Stokes/Allen-Cahn system in a two dimensional, bounded and smooth domain, when a parameter $\varepsilon>0$ that is proportional to the thickness of the diffuse interface tends to zero rigorously. We prove convergence of the solutions of the Navier-Stokes/Allen-Cahn system to solutions of a sharp interface model, where the interface evolution is given by the mean curvature flow with an additional convection term coupled to a two-phase Navier-Stokes system with surface tension. This is done by constructing an approximate solution from the limiting system via matched asymptotic expansions together with a novel Ansatz for the highest order term, and then estimating its difference with the real solution with the aid of a refined spectral estimate of the linearized Allen-Cahn operator near the approximate solution.
Stokes/CahnâHilliard 系统的尖锐接口限制，第二部分：近似解
影响因子：
1.3
作者：
H. Abels;A. Marquardt
通讯作者：
A. Marquardt
AllenâCahn 方程收敛到二维 90o 接触角的平均曲率流
影响因子：
1
作者：
H. Abels;M. Moser
通讯作者：
M. Moser