题 目 二:Recent progress on analysis and computation for two-phase flows with moving contact line
摘 要 二: It is a challenging problem to model and simulate two-phase flows with moving contact line. The standard no-slip boundary condition will lead to infinite energy dissipations. This is referred to as the moving contact line paradox. Although many continuum models have been developed to resolve the paradox, there still exist many controversies. Mathematically, the moving contact line problem is described by a two-phase Navier-Stokes system coupled with some nonlinear dynamic boundary conditions. Both analysis and simulation for the system are very challenging. In this talk, I will present recent progress on modelling, analysis and numerical simulations to the problem, especially for the case that the solid substrate is rough or inhomogeneous. I will also address the main difficulties we have encountered in this field.