薄膜流动中接触线奇异性的动力系统方法
A dynamical systems approach for the contact-line singularity in thin-film flows
摘要：
我们感兴趣的是一个完整的表征接触线奇异性的薄膜流为零和非零接触角。通过处理模型问题的源型自相似解决方案，我们表明，这种奇异性可以理解的不变流形的一个合适的动力系统的研究。特别是，我们证明了一个广泛的一类流动性指数和零和非零动态接触角的接触线附近的奇异扩展的规律性结果。关键点是中心流形的简化和确定平衡点的共振条件。结果被扩展到更高维度的径向对称源型解决方案。此外，我们给出了动力系统证明的自相似液滴解的存在性和唯一性的非零动态接触角的情况。
英文摘要：
We are interested in a complete characterization of the contact-line singularity of thin-film flows for zero and nonzero contact angles. By treating the model problem of source-type self-similar solutions, we demonstrate that this singularity can be understood by the study of invariant manifolds of a suitable dynamical system. In particular, we prove regularity results for singular expansions near the contact line for a wide class of mobility exponents and for zero and nonzero dynamic contact angles. Key points are the reduction to center manifolds and identifying resonance conditions at equilibrium points. The results are extended to radially-symmetric source-type solutions in higher dimensions. Furthermore, we give dynamical systems proofs for the existence and uniqueness of self-similar droplet solutions in the nonzero dynamic contact-angle case.
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