体-面相互作用下不可压缩两相流扩散界面模型的Voigt正则化的全局拟强解
Global Quasi-strong Solutions to the Voigt Regularization of a Diffuse Interface Model for Incompressible Two-phase Flows with Bulk-surface Interaction
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中文总结 AI 辅助
本文研究带体-面相互作用的不可压缩两相流扩散界面模型，结合逼近格式与半Galerkin方法，证明其全局拟强解存在性，该解满足能量等式。
中文摘要 AI 辅助
我们在光滑有界区域Ω⊂ℝᵈ（d=2,3）中分析了一种热力学一致的不可压缩、密度不匹配的两相粘性流扩散界面模型。该模型由速度场的Navier-Stokes-Voigt方程和相场变量的带奇异势的对流Cahn-Hilliard方程组成。所得流体力学系统受速度场的广义Navier滑移边界条件，以及相场变量和化学势的Cahn-Hilliard型动态边界条件约束。借助Voigt正则化，我们通过结合精细的逼近格式和半Galerkin方法，建立了满足能量等式的全局拟强解的存在性。
英文摘要
We analyze a thermodynamically consistent diffuse interface model for incompressible two-phase viscous flows with unmatched densities in a smooth bounded domain $Ω\subset\mathbb{R}^d$ $(d=2,3)$. This model consists of the Navier-Stokes-Voigt equations for the velocity field and a convective Cahn-Hilliard equation with a singular potential for the phase-field variable. The resulting hydrodynamic system is subject to a generalized Navier slip boundary condition for the velocity field and Cahn-Hilliard-type dynamic boundary conditions for the phase-field variable and the chemical potential. With the aid of the Voigt regularization, we establish the existence of global quasi-strong solutions that satisfy an energy equality. This is achieved through a combination of delicate approximation schemes and a semi-Galerkin method.
