论文标题
在另一种粘性流体内的粘性流薄层的动力学上
On the dynamics of thin layers of viscous flows inside another viscous fluid
论文作者
论文摘要
在这项工作中，我们将研究粘液液的薄层的动力学，该粘性流体嵌入了另一种粘性流体的内部。可以通过stokes方程的自由边界问题的解决方案近似所得的流，其中未知数之一是曲线的形状，曲线的形状近似于流体薄层的几何形状。我们还得出了产生该流体厚度的方程式。将使用匹配的渐近扩展来得出此模型，称为几何无边界问题。我们将证明，只要存在几何不含自由边界问题的解决方案，我们就会证明良好的几何边界问题是很好的提出，并且厚度方程的解决方案得到了很好的定义（特别是它们不会屈服于流体层的破裂）。
In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the Stokes equation in which one of the unknowns is the shape of a curve which approximates the geometry of the thin layer of fluid. We also derive the equation yielding the thickness of this fluid. This model, that will be termed as the Geometric Free Boundary Problem, will be derived using matched asymptotic expansions. We will prove that the Geometric Free Boundary Problem is well posed and the solutions of the thickness equation are well defined (in particular they do not yield breaking of fluid layers) as long as the solutions of the Geometric Free Boundary Problem exist.
