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

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)818-891
Number of pages74
JournalCommunications on Pure and Applied Mathematics
Volume75
Issue number4
DOIs
StatePublished - Apr 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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