发表机构
Politecnico di Milano; Fudan University（米兰理工大学; 复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文研究含可溶表面活性剂不可压缩两相流热力学一致扩散界面模型的强适定性，证明三维局部与二维全局强解存在性及唯一性，并推广至浓度依赖迁移率情形。
AI 中文摘要
我们考虑一个针对含可溶表面活性剂的不可压缩粘性牛顿流体二元混合物的热力学一致扩散界面模型。该流体动力学系统通过纳入一个关于表面活性剂浓度的附加Cahn-Hilliard方程，推广了针对密度不匹配两相流的Abels-Garcke-Grün模型。我们研究具有物理相关奇异势的初边值问题的强适定性，其中流体速度满足无滑移边界条件，相场变量及相应化学势满足齐次Neumann边界条件。首先，我们建立了三维情形下局部时间强解的存在性和二维情形下全局时间强解的存在性。在二维情形下，我们进一步证明，在关于奇异势的自然增长假设下，强解保持严格远离纯相，从而保证唯一性。在三维情形下，我们建立了强解的局部时间唯一性，前提是初始数据严格远离纯相。我们的结果将先前关于Abels-Garcke-Grün模型强解的工作从常迁移率的特殊情形推广到具有浓度依赖迁移率及与表面活性剂相互作用的更一般情形。
英文摘要
We consider a thermodynamically consistent diffuse-interface model for binary mixtures of incompressible viscous Newtonian fluids with a soluble surfactant. This hydrodynamic system generalizes the Abels-Garcke-Grün model for two-phase flows with unmatched densities by incorporating an additional Cahn-Hilliard equation for the surfactant concentration. We study the strong well-posedness of the initial-boundary value problem with physically relevant singular potentials, subject to a no-slip boundary condition for the fluid velocity and homogeneous Neumann boundary conditions for the phase-field variables and the corresponding chemical potentials. First, we establish the existence of local-in-time strong solutions in three dimensions and global-in-time strong solutions in two dimensions. In the two-dimensional case, we further show that, under natural growth assumptions on the singular potentials, strong solutions remain strictly separated from the pure phases, thereby guaranteeing uniqueness. In the three-dimensional case, we establish local-in-time uniqueness of strong solutions, provided that the initial data are strictly separated from the pure phases. Our results extend previous work on strong solutions to the Abels-Garcke-Grün model from the special case of constant mobility to the more general scenario with concentration-dependent mobilities and interactions with a surfactant.
