体-表面Navier-Stokes-Cahn-Hilliard模型：弱解的存在性与渐近极限
On a bulk-surface Navier-Stokes-Cahn-Hilliard model: Existence of weak solutions and asymptotic limits
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中文总结 AI 辅助
本文针对含移动接触线等特征的两相流，研究体-表面Navier-Stokes-Cahn-Hilliard模型，建立其全局弱解存在性，并分析高摩擦与解耦极限下的渐近行为，相关收敛性证明含具独立价值的Mosco收敛结果。
中文摘要 AI 辅助
本文研究热力学一致的体-表面Navier-Stokes-Cahn-Hilliard系统，该系统描述具有移动接触线、可变接触角和质量传递的两相流。我们针对非退化迁移率函数和奇异自由能势，建立了全局弱解的存在性。证明基于隐式时间离散格式及体-表面自由能凸部分的次微分刻画。最后，我们研究同时高摩擦与解耦极限，证明对应的弱解在子序列意义下收敛到Abels-Garcke-Grün模型的弱解。证明的一个关键要素是体-表面自由能凸部分的Mosco收敛，这一结果可能具有独立研究价值。
英文摘要
We study a thermodynamically consistent bulk-surface Navier--Stokes--Cahn--Hilliard system describing two-phase flows exhibiting moving contact lines, variable contact angles, and mass transfer. We establish the existence of global weak solutions for non-degenerate mobility functions and singular free-energy potentials. The proof is based on an implicit time-discretization scheme and a subdifferential characterization of the convex part of the bulk-surface free energy. Finally, we study the simultaneous high-friction and decoupling limit, and prove that corresponding weak solutions converge, up to a subsequence, to a weak solution of the Abels--Garcke--Grün model. One key ingredient of the proof is the Mosco convergence of the convex part of the bulk-surface free energy, which might be of independent interest.
