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Publication 16-CNA-031
Yunrui Zheng Ian Tice Abstract: 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 |