In an effort to study the stability of contact lines in fluids, we consider the dynamics of a drop of incompressible viscous Stokes fluid evolving above a one-dimensional flat surface under the influence of gravity. This is a free boundary problem: the interface between the fluid on the surface and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase interface where the fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free interface and the flat surface is called the contact angle. We consider a model of this problem that allows for fully dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then allow us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that decay to a shifted equilibrium exponentially fast.

中文翻译：

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具有接触点的静滴的动力学和稳定性

为了研究流体中接触线的稳定性，我们考虑了一滴不可压缩的粘性斯托克斯流体在重力影响下在一维平面上方演化的动力学。这是一个自由边界问题：表面上的流体和上面的空气（由微不足道的流体建模）之间的界面可以自由移动并受到毛细管力。流体、空气和固体容器壁相交的三相界面称为接触点，自由界面与平面之间形成的夹角称为接触角。我们考虑这个问题的模型，它允许完全动态的接触点和角度。我们为模型开发了一个先验估计方案，然后我们可以证明对于足够接近均衡的初始数据，