论文标题
涡流贴片编排，用于活动标量方程
Vortex patches choreography for active scalar equations
论文作者
论文摘要
本文介绍了位于常规多边形顶点的$ n $涡旋贴片的存在，其$ n $侧面以恒定的角速度旋转多边形旋转。这是为Euler和（SQG）$_β$方程式完成的，其中$β\ in（0,1）$，但也可能扩展到更通用的模型。这个想法是$ n $ point涡流系统的Thomsom Polygon的降低化，即，位于带有$ n $侧的普通多边形顶点的$ n $ point涡流。该证明基于对轮廓动力学方程的研究，并结合了无限尺寸隐式函数定理的应用和函数空间的井。
This paper deals with the existence of $N$ vortex patches located at the vertex of a regular polygon with $N$ sides that rotate around the center of the polygon at a constant angular velocity. That is done for Euler and (SQG)$_β$ equations, with $β\in(0,1)$, but may be also extended to more general models. The idea is the desingularization of the Thomsom polygon for the $N$ point vortex system, that is, $N$ point vortices located at the vertex of a regular polygon with $N$ sides. The proof is based on the study of the contour dynamics equation combined with the application of the infinite dimensional Implicit Function theorem and the well--chosen of the function spaces.
