论文标题
Lagrangian配方中3D不可压缩的Euler方程的明确解决方案
Explicit solutions to the 3D incompressible Euler equations in Lagrangian formulation
论文作者
论文摘要
我们使用拉格朗日框架将许多显式解决方案的家族介绍给三维不可压缩的欧拉方程。在本研究之前的文献中，文献中几乎没有确切的拉格朗日解决方案。我们搜索时间组件和空间组件分开的解决方案，应用与以前在二维情况下使用的相同想法。我们展示了一种通用方法，可以得出空间组件和时间组件的单独约束方程。使用此功能为我们提供了大量的解决方案集，这些解决方案集表现出几种不同类型的流体行为，但是由于它们在计算上进行分析，因此我们必须仅将更深入的分析限制在最有趣的情况下。也可能有可能存在更多的变量类型分离的解决方案，而不是我们发现的。
We introduce many families of explicit solutions to the three dimensional incompressible Euler equations for nonviscous fluid flows using the Lagrangian framework. Almost no exact Lagrangian solutions exist in the literature prior to this study. We search for solutions where the time component and the spatial component are separated, applying the same ideas we used previously in the two dimensional case. We show a general method to derive separate constraint equations for the spatial component and the time component. Using this provides us with a plenty of solution sets exhibiting several different types of fluid behaviour, but since they are computationally heavy to analyze, we have to restrict deeper analysis to the most interesting cases only. It is also possible and perhaps even probable that there exist more solutions of the separation of variables type beyond what we have found.
