非平凡无旋流附近的定常涡斑
Steady vortex patches near a nontrivial irrotational flow
摘要：
本文研究了平面有界区域中理想流体中的涡斑问题。通过求解一个极小化问题并研究极小值的极限行为，证明了对于任意一个非平凡无旋流对应的调和函数$q$，在区域边界上存在一族稳定的涡斑逼近$q$的极值点集.此外，我们表明，每一个有限的严格极值点的$q$对应于一个家庭的稳定多涡补丁接近它。
英文摘要：
In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the minimizer, we prove that for any harmonic function $q$ corresponding to a nontrivial irrotational flow, there exists a family of steady vortex patches approaching the set of extremum points of $q$ on the boundary of the domain. Furthermore, we show that each finite collection of strict extreme points of $q$ corresponds to a family of steady multiple vortex patches approaching it.
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