论文标题
湖泊方程的几个点涡流的动力学
Dynamics of several point vortices for the lake equations
论文作者
论文摘要
严格得出了湖泊方程的点涡旋的全球渐近动力学。事实证明，最初将涡度集中在$ n $ dintiond的涡流中心左右的涡度始终始终保持集中。具体而言，我们证明了涡度的弱浓度及其在深度功能最陡峭上升方向上的强浓度。结果，我们在领先顺序的深度函数的水平线上获得了点涡旋的运动定律。在第二个方向上缺乏强大的定位与涡流现象有关。主要结果允许考虑要考虑初始数据的浓度属性的任何固定数量的涡流和一般假设。不需要进一步的属性，例如特定轮廓或数据对称性。我们的分析中包括边界上的消失地形。我们的方法的灵感来自3D轴对称不可压缩流体中涡旋环的演变的最新结果。
The global asymptotic dynamics of point vortices for the lake equations is rigorously derived. Vorticity that is initially sharply concentrated around $N$ distinct vortex centers is proven to remain concentrated for all times. Specifically, we prove weak concentration of the vorticity and in addition strong concentration in the direction of the steepest ascent of the depth function. As a consequence, we obtain the motion law of point vortices following at leading order the level lines of the depth function. The lack of strong localization in the second direction is linked to the vortex filamentation phenomena. The main result allows for any fixed number of vortices and general assumptions on the concentration property of the initial data to be considered. No further properties such as a specific profile or symmetry of the data are required. Vanishing topographies on the boundary are included in our analysis. Our method is inspired by recent results on the evolution of vortex rings in 3D axisymmetric incompressible fluids.
