Axi‐symmetrization near Point Vortex Solutions for the 2D Euler Equation

  title={Axi‐symmetrization near Point Vortex Solutions for the 2D Euler Equation},
  author={A. D. Ionescu and Hao Jia},
  journal={Communications on Pure and Applied Mathematics},
  • A. Ionescu, H. Jia
  • Published 19 April 2019
  • Mathematics
  • Communications on Pure and Applied Mathematics
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… 
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