基于混合物理论的两相流扩散界面模型的局部适定性
Local Well-Posedness for a Diffuse Interface Model for Two-Phase Flows from Mixture Theory
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中文总结 AI 辅助
本文针对ten Eikelder等人提出的混合物理论框架下的两相流扩散界面模型，建立了其时间局部适定性，采用不动点策略完成证明，是该模型的首次分析研究。
中文摘要 AI 辅助
本文针对新近提出的描述不可压缩两相流的扩散界面模型，建立了时间局部适定性结果。该结果是对ten Eikelder等人提出的模型开展的首次分析研究，该模型用于描述宏观不可混溶、粘性、不可压缩且密度不匹配的二元混合物的运动。与基于单一平均速度的经典扩散界面模型不同，该模型在混合物理论框架内推导，为每一相分配各自的动量和质量平衡，由此得到由两个耦合的纳维-斯托克斯方程和两个质量输运方程组成的系统。适定性结果的证明采用不动点策略，其中主要难点在于对相关线性化系统主部的分析。
英文摘要
Local-in-time well-posedness is established for a recently proposed diffuse interface model describing incompressible two-phase flows. The result constitutes the first analytical study of a model introduced by ten Eikelder et al. for the motion of a binary mixture of macroscopically immiscible, viscous, incompressible fluids with unmatched densities. In contrast to classic diffuse interface models based on a single mean velocity, this model is derived within the framework of mixture theory, assigning each phase its own momentum and mass balance, which results in a system of two coupled Navier--Stokes equations and two mass transport equations. The proof of the well-posedness result uses a fixed-point strategy, where the main difficulty lies in the analysis of the principal part of the associated linearized system.
