科研之友
微信
新浪微博
Facebook
分享链接
摘要
We establish well-posedness for the family of thin-film equations with . The model (1) with has been used to describe the evolution of a capillary driven thin liquid droplet on a solid substrate in terms of its height profile . The family of thin-film equations (1) provides a model problem to investigate contact line propagation in fluid dynamics under relaxed slip conditions. The parabolicity of the fourth order parabolic problem degenerates at the free boundary, which leads to a loss of regularity at the moving contact point. Our solutions are regular in terms of the two variables d(x) and d(x)(3-n) , where d(x) is the distance to the free boundary. The main technical difficulty in the analysis of (1) is related to the loss of regularity at the contact points.
- 出版日期2015-11
