论文标题
浓缩涡流对的渐近估计值
Asymptotic estimates for concentrated vortex pairs
论文作者
论文摘要
在[comm。数学。物理。 324（2013），445--463]，Burton-Lopes Filho-Nussenzveig Lopes研究了缓慢行进的涡旋对的存在和稳定性，因为脉冲相对于规定的重排阶层而受到脉冲相对于脉冲的最大惩罚。在本文中，我们证明，经过适当的缩放转化后，伯顿 - 洛佩斯菲尔霍·纳森氏菌所研究的最大化问题实际上导致了一个集中涡流对的家族，接近一对相同尺寸和相反符号的点涡流。证明的关键要素是针对缩放最大化器的支撑物的大小推断出统一的结合。
In [Comm. Math. Phys. 324 (2013), 445--463], Burton-Lopes Filho-Nussenzveig Lopes studied the existence and stability of slowly traveling vortex pairs as maximizers of the kinetic energy penalized by the impulse relative to a prescribed rearrangement class. In this paper, we prove that after a suitable scaling transformation the maximization problem studied by Burton-Lopes Filho-Nussenzveig Lopes in fact gives rise to a family of concentrated vortex pairs approaching a pair of point vortices with equal magnitude and opposite signs. The key ingredient of the proof is to deduce a uniform bound for the size of the supports of the scaled maximizers.
