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 \(\text {(SQG)}_\beta \) equations, with \(\beta \in (0,1)\), 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.

这篇论文讨论了N 个漩涡斑块的存在，它位于一个有N 条边的正多边形的顶点处，这些多边形以恒定角速度围绕多边形的中心旋转。这是为 Euler 和\(\text {(SQG)}_\beta \)方程完成的，带有\(\beta \in (0,1)\)，但也可以扩展到更一般的模型。思路是将Thomsom多边形解奇异化为N点涡旋系统，即N个点涡旋位于正多边形的顶点处，其中N个边。证明是基于轮廓动力学方程的研究，结合无限维隐函数定理的应用和函数空间的精心选择。