空心涡的去奇异化和整体延拓
Desingularization and global continuation for hollow vortices
摘要：
空心涡是一个由涡面包围的恒压区域，悬浮在理想流体中;因此可以解释为水中旋转的气泡。本文给出了将非退化定常点涡位形去奇异化为定常空心涡集合的一般方法。我们的机器同时处理平移，旋转和静止状态。通过全局分歧理论，我们进一步得到了解的极大曲线，这些曲线一直持续到奇点的出现。作为具体的例子，我们给出了同向旋转空心涡对和静止空心涡三极的第一存在性理论，以及Pocklington经典同向平移空心涡对的新构造。所有这些家庭扩展到非微扰制度，我们得到了一个相当完整的表征的限制行为沿全球分歧曲线。
英文摘要：
A hollow vortex is a region of constant pressure bounded by a vortex sheet and suspended inside a perfect fluid; it can therefore be interpreted as a spinning bubble of air in water. This paper gives a general method for desingularizing non-degenerate steady point vortex configurations into collections of steady hollow vortices. Our machinery simultaneously treats the translating, rotating, and stationary regimes. Through global bifurcation theory, we further obtain maximal curves of solutions that continue until the onset of a singularity. As specific examples, we give the first existence theory for co-rotating hollow vortex pairs and stationary hollow vortex tripoles, as well as a new construction of Pocklington's classical co-translating hollow vortex pairs. All of these families extend into the non-perturbative regime, and we obtain a rather complete characterization of the limiting behavior along the global bifurcation curve.
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