# 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…

## 5 Citations

### Canonical scale separation in two-dimensional incompressible hydrodynamics

- PhysicsJournal of Fluid Mechanics
- 2022

It is shown that Euler’s equations posses an intrinsic, canonical splitting of the vorticity function, which accounts for the “broken line” in the power law for the energy spectrum, observed in both experiments and numerical simulations.

### Platonic Solids and Symmetric Solutions of the N-vortex Problem on the Sphere

- MathematicsJournal of Nonlinear Science
- 2022

We consider the N-vortex problem on the sphere assuming that all vortices have equal strength. We develop a theoretical framework to analyse solutions of the equations of motion with prescribed…

### Geometric Hydrodynamics in Open Problems

- Mathematics
- 2022

Geometric Hydrodynamics has ﬂourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with several new constructions in ﬂuid dynamics…

### On Maximally Mixed Equilibria of Two-Dimensional Perfect Fluids

- MathematicsArchive for Rational Mechanics and Analysis
- 2022

The vorticity of a two-dimensional perfect (incompressible and inviscid) fluid is transported by its area preserving flow. Given an initial vorticity distribution ω0\documentclass[12pt]{minimal}…

### Vortex Motion of the Euler and Lake Equations

- Physics, MathematicsJournal 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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