标题： 不可压缩极限的强解到两相流的扩散界面模型 显示英文标题

标题： Incompressible Limit of Strong Solutions to the Diffuse Interface Model for Two-phase Flows

摘要： 本文研究了在周期性边界条件下可压缩两相流模型的不可压缩极限问题，其中纳维-斯托克斯方程与Cahn-Hilliard方程或Allen-Cahn方程非线性耦合。粘度系数允许同时依赖于密度和相场变量。我们建立了当马赫数趋于零时，可压缩系统的局部和全局强解对不可压缩系统的严格收敛性。这一理论框架在可压缩和不可压缩相场模型之间建立了必要的联系，证明了两种形式在捕捉界面流动动力学方面表现出一致的物理保真度。此外，我们还提供了一些解的收敛速率估计。 显示英文摘要

摘要： This paper is concerned with the incompressible limit problem for strong solutions of compressible two-phase flow models under periodic boundary conditions, where the Navier-Stokes equations are nonlinearly coupled with either Cahn-Hilliard equations or Allen-Cahn equations. The viscosity coefficients are allowed to depend both on the density and the phase field variable. We establish rigorous convergence of both local and global strong solutions of compressible systems to their incompressible systems as the Mach number tends to zero.This theoretical framework establishes an essential linkage between compressible and incompressible phase field models, demonstrating that both formulations exhibit consistent physical fidelity in capturing interfacial flow dynamics.Furthermore, we provide some convergence rate estimates of the solutions.