论文标题
液体中接触线的稳定性：2D Navier-Stokes流量
Stability of contact lines in fluids: 2D Navier-Stokes flow
论文作者
论文摘要
在本文中，我们研究了不可压缩的粘性流体在二维的开放式容器中演变的动力学。流体力学由Navier-Stokes方程决定。流体的上边界是自由的，并且在容器内演变。流体由均匀的重力场作用，毛细管沿自由边界进行解释。三相界面的界面，在容器上方的流体，空气和固体容器壁接触称为接触点，在接触点处形成的角度称为接触角。我们考虑的模型集成了边界条件，允许接触点和角度的全部运动。平衡构型由一个域内的静态流体组成，该域的上边界作为函数的图表最小化重力毛细管能量功能，但要受固定质量约束。平衡触点角可以根据毛细管参数的选择在$ 0 $和$π$之间的任何值。本文的主要目的是开发先验估计的方案，该方案表明，从全球范围内足够接近平衡的数据发出的溶液在全球范围内存在，并以指数率的速率衰减至平衡。
In this paper we study the dynamics of an incompressible viscous fluid evolving in an open-top container in two dimensions. The fluid mechanics are dictated by the Navier-Stokes equations. The upper boundary of the fluid is free and evolves within the container. The fluid is acted upon by a uniform gravitational field, and capillary forces are accounted for along the free boundary. The triple-phase interfaces where the fluid, air above the vessel, and solid vessel wall come in contact are called contact points, and the angles formed at the contact point are called contact angles. The model that we consider integrates boundary conditions that allow for full motion of the contact points and angles. Equilibrium configurations consist of quiescent fluid within a domain whose upper boundary is given as the graph of a function minimizing a gravity-capillary energy functional, subject to a fixed mass constraint. The equilibrium contact angles can take on any values between $0$ and $π$ depending on the choice of capillary parameters. The main thrust of the paper is the development of a scheme of a priori estimates that show that solutions emanating from data sufficiently close to the equilibrium exist globally in time and decay to equilibrium at an exponential rate.
