论文标题
Navier的尖锐界面限制 - 史托克斯/Allen- -CAHN系统，具有恒定的迁移率：通过相对能量方法收敛速率
The sharp interface limit of a Navier--Stokes/Allen--Cahn system with constant mobility: Convergence rates by a relative energy approach
论文作者
论文摘要
我们研究了一个分散接口系统的尖锐接口限制，该系统将Allen-cahn方程与构造Navier耦合 - 在$ \ Mathbb {r}^d $中与$ d \ in \ in \ {2,3 \} $中的有限域中的Stokes System。该模型用于描述粘性不可压缩流中的传播前部，其过渡层的宽度以小参数$ \ varepsilon> 0 $为特征。我们表明，解决方案会融合到限制的两相流体系统，其表面张力将平均曲率流和Navier - Stokes System融合。主要假设是极限系统的演变足够规律，并且相关的演变界面不会与容器的边界相交。对于定量准备好的初始数据，我们甚至建立了最佳的收敛速率。这是这种严格的结果，在所有与物理相关的环境维度中都是有效的。
We investigate the sharp interface limit of a diffuse interface system that couples the Allen--Cahn equation with the instationary Navier--Stokes system in a bounded domain in $\mathbb{R}^d$ with $d \in \{2,3\}$. This model is used to describe a propagating front in a viscous incompressible flow with the width of the transition layer being characterized by a small parameter $\varepsilon>0$. We show that the solutions converge to a limit two-phase fluid system with surface tension that couples the mean curvature flow and the Navier--Stokes system. The main assumptions are that the evolution of the limit system is sufficiently regular and that the associated evolving interface does not intersect the boundary of the container. For quantitatively well-prepared initial data, we even establish an optimal convergence rate. This is the first rigorous result of this kind which is valid in all physically relevant ambient dimensions.
