论文标题
Navier-Stokes/Allen-Cahn系统的尖锐接口限制具有不同的粘度
Sharp Interface Limit for a Navier-Stokes/Allen-Cahn System with Different Viscosities
论文作者
论文摘要
当参数$ \ varepsilon> 0 $时，与与差异差异接口的厚度成正比时，我们讨论了在二维，有界和光滑的域中耦合的Navier-Stokes/Allen-Cahn系统的尖锐接口极限。我们证明了Navier-Stokes/Allen-Cahn系统的解决方案与尖锐界面模型的解决方案的融合，其中界面演化是由平均曲率流的额外对流术语给出的，并带有额外的对流术语，并耦合到具有表面张力的两相Navier-Stokes System。这是通过通过匹配的渐近扩展以及新的ANSATZ与最高级项一起构建限制系统中的近似解决方案，然后借助于近似解决方案的线性化Allen-CAHN操作员的精制频谱估计其与真实解决方案的差异来完成。
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.
