AI 中文总结
研究复杂流体相分离受流体动力学影响的问题，提出由输运噪声驱动的Cahn-Hilliard模型，在热力学相关框架下分析，考虑不同形式噪声，首次在二维和三维建立系统适定性及热力学一致性。
AI 中文摘要
复杂流体中发生的相分离现象对流体动力学效应敏感：当二元流体混合物经历旋节线分解时，新出现的畴模式不再仅由界面动力学决定，而是会因平流而重塑。在一些应用中，平流效应甚至可能引发湍流，进一步在广泛空间尺度上影响分离过程。基于此背景，我们提出了一个由输运噪声驱动的Cahn-Hilliard模型，该模型能够捕捉湍流的内在随机性。我们在热力学相关框架下对该模型进行分析，采用奇异的弗洛里-哈金斯势和可能退化的迁移率，并考虑伊藤和斯特拉托诺维奇形式的噪声。在这项工作中，作为第一步研究，我们在二维和三维空间中建立了系统的适定性及其热力学一致性。
英文摘要
Phase separation phenomena occurring in complex fluids are known to be sensitive to hydrodynamic effects: when a binary fluid mixture undergoes spinodal decomposition, the emerging pattern of domains is no longer dictated by interfacial dynamics alone, but is reshaped by advection. In several applications of interest, advection effects may even cause the onset of turbulence, further affecting the segregation process on a wide range of spatial scales. Motivated by this, we propose a Cahn-Hilliard model driven by transport noise able to capture the intrinsic stochasticity of turbulence. The model is analyzed in its thermodynamically-relevant framework, namely employing a singular Flory-Huggins potential and a possibly degenerate mobility, and the noise is considered both in Ito and Stratonovich form. In this work, as a first-step investigation, we establish well-posedness of the system in two and three spatial dimensions and its thermodynamical consistency.
Comments49 pp
