论文标题
全球分叉，用于旋转和反旋转涡流对
Global bifurcation for corotating and counter-rotating vortex pairs
论文作者
论文摘要
Hmidi和Mateu通过一对点涡流的降低化证明了固定和反向旋转涡流对的局部曲线的存在。在本文中，我们构建了这些局部曲线的全球延续。也就是说，我们考虑的解决方案不仅仅是琐碎解决方案的扰动。确实，尽管局部分析依赖于琐碎解决方案的线性方程的研究，但全局分析需要对非线性问题的拓扑特性有更深入的了解。为了证明我们，由于Buffoni和Toland，我们适应了强大的分析全局分叉定理，以使分叉点的奇异性。对于固定和反向旋转对的，沿解决方案的全局曲线，角流体速度消失或两个斑块自相隔。
The existence of a local curve of corotating and counter-rotating vortex pairs was proven by Hmidi and Mateu in via a desingularization of a pair of point vortices. In this paper, we construct a global continuation of these local curves. That is, we consider solutions which are more than a mere perturbation of a trivial solution. Indeed, while the local analysis relies on the study of the linear equation at the trivial solution, the global analysis requires on a deeper understanding of topological properties of the nonlinear problem. For our proof, we adapt the powerful analytic global bifurcation theorem due to Buffoni and Toland, to allow for the singularity at the bifurcation point. For both the corotating and the counter-rotating pairs, along the global curve of solutions either the angular fluid velocity vanishes or the two patches self-intersect.
