We prove asymptotic stability of point vortex solutions to the full Euler equation in two dimensions. More precisely, we show that a small, Gevrey smooth, and compactly supported perturbation of a point vortex leads to a global solution of the Euler equation in 2D, which converges weakly as t → ∞ to a radial profile with respect to the vortex. The position of the point vortex, which is time dependent, stabilizes rapidly and becomes the center of the final, radial profile. The mechanism that leads to stabilization is mixing and inviscid damping. © 2021 Wiley Periodicals LLC.

中文翻译：

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二维欧拉方程的点涡解附近的轴对称化

我们证明了二维全欧拉方程的点涡解的渐近稳定性。更准确地说，我们证明了一个小的、Gevrey 平滑和紧凑支持的点涡扰动导致了欧拉方程在 2D 中的全局解，当t  → ∞时，它弱收敛到相对于涡旋的径向轮廓。与时间相关的点涡的位置迅速稳定并成为最终径向剖面的中心。导致稳定的机制是混合和非粘性阻尼。© 2021 威利期刊有限责任公司。