论文标题
周期性涡流补丁和图层的轮廓动力学和全球规律性
Contour dynamics and global regularity for periodic vortex patches and layers
论文作者
论文摘要
我们研究了2D不可压缩的Euler方程的涡旋斑块。关于此问题的先前工作以涡度（即涡旋补丁）为有限区域的支持。相反，我们考虑水平周期性设置。这既包括有界涡流贴片的周期性数组和垂直界限层的情况。我们在此水平周期性设置中为贴片边界开发了轮廓动力学方程，并演示了该补丁边界的全局$ c^{1，ε} $。在提出问题的过程中，我们考虑了2D不可压缩的Euler方程的周期性解决方案的不同概念，并证明了这些方程的等效性。
We study vortex patches for the 2D incompressible Euler equations. Prior works on this problem take the support of the vorticity (i.e., the vortex patch) to be a bounded region. We instead consider the horizontally periodic setting. This includes both the case of a periodic array of bounded vortex patches and the case of vertically bounded vortex layers. We develop the contour dynamics equation for the boundary of the patch in this horizontally periodic setting, and demonstrate global $C^{1,ε}$ regularity of this patch boundary. In the process of formulating the problem, we consider different notions of periodic solutions of the 2D incompressible Euler equations, and demonstrate equivalence of these.
