Integrability of Point-Vortex Dynamics via Symplectic Reduction: A Survey

@article{Modin2020IntegrabilityOP,
  title={Integrability of Point-Vortex Dynamics via Symplectic Reduction: A Survey},
  author={Klas Modin and Milo Viviani},
  journal={Arnold Mathematical Journal},
  year={2020},
  volume={7},
  pages={357 - 385}
}
Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on two-dimensional manifolds. Integrability results for few point-vortices on various domains is a vivid topic, with many results and techniques scattered in the literature. Here, we give a unified framework for proving integrability results for N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage… 

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  • Cheng Yang
  • Physics, Mathematics
    Journal of Nonlinear Science
  • 2021
It is proved that the 2-vortex system in the half-plane is nonintegrable for $N>2$ and the skew-mean-curvature flow in R^n, n with certain symmetry can be regarded as point vortex motion of the 2D lake equations.

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