Axi‐symmetrization near Point Vortex Solutions for the 2D Euler Equation
Axi‐symmetrization near Point Vortex Solutions for the 2D Euler Equation
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DOI：
10.1002/cpa.21974
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发表时间：
2019-04
影响因子：
3
通讯作者：
A. Ionescu;H. Jia
中科院分区：
文献类型：
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作者：
A. Ionescu;H. Jia
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，我们证明了点涡旋的小的、Gevrey光滑的和紧支撑的扰动导致了二维欧拉方程的整体解，该整体解以t→∞弱收敛到相对于该涡旋的径向轮廓。与时间相关的点涡旋的位置迅速稳定，并成为最终的径向轮廓的中心。稳定的机理是混合和无粘阻尼力。©2021威利期刊有限责任公司。
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.