In this paper, we prove nonlinear stability of planar vortex patches concentrated near a non-degenerate minimum point of the Robin function in a general bounded domain. These vortex patches are stationary solutions of the two-dimensional incompressible Euler equations. The result is obtained by showing that these concentrated vortex patches are in fact isolated maximizers of the kinetic energy among isovortical patches.

中文翻译：

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理想流体中平面涡旋斑的非线性稳定性

在本文中，我们证明了平面涡旋斑片的非线性稳定性集中在一般有界域中的Robin函数的非退化最小点附近。这些涡旋斑是二维不可压缩的欧拉方程的平稳解。通过显示这些浓缩的涡旋斑片实际上是等涡旋斑片中动能的孤立的最大化子而获得了结果。