Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 16-CNA-031 Local Well-Posedness Of The Contact Line Problem In 2-D Stokes Flow Yunrui ZhengBeijing International Center for Mathematical Research Peking University Beijing, 100871, P. R. Chinaruixue@mail.ustc.edu.cn Ian TiceDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213ian.tice@andrew.cmu.eduAbstract: We consider the evolution of contact lines for viscous fluids in a two-dimensional open-top vessel. The domain is bounded above by a free moving boundary and otherwise by the solid wall of the vessel. The dynamics of the fluid are governed by the incompressible Stokes equations under the in influence of gravity, and the interface between fluid and air is under the effect of capillary forces. Here we develop a local well- posedness theory of the problem in the framework of nonlinear energy methods. We utilize several techniques, including: energy estimates of a geometric formulation of the Stokes equations, a Galerkin method with a time-dependent basis for an $\epsilon$-perturbed linear Stokes problem in moving domains, the contraction mapping principle for the $\epsilon$-perturbed nonlinear full contact line problem, and a continuity argument for uniform energy estimates.Get the paper in its entirety as  16-CNA-031.pdf