Burst of Point Vortices and Non-Uniqueness of 2D Euler Equations

Abstract

We give a rigorous construction of solutions to the Euler point vortices system in which three vortices burst out of a single one in a configuration of many vortices, or equivalently that there exist configurations of arbitrarily many vortices in which three of them collapse in finite time. As an intermediate step, we show that well-known self-similar bursts and collapses of three isolated vortices in the plane persist under a sufficiently regular external perturbation. We also discuss how our results produce examples of non-unique weak solutions to 2-dimensional Euler's equations -- in the sense introduced by Schochet -- in which energy is dissipated.

arXiv comment30 pages

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Cited by in corpus (7)

• Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise
• Hölder regularity for collapses of point vortices
• Effect of Transport Noise on Kelvin-Helmholtz instability
• Gibbs Equilibrium Fluctuations of Point Vortex Dynamics
• Decay of Time Correlations in Point Vortex Systems
• On the Dynamics of Point Vortices with Positive Intensities collapsing with the boundary
• Random Splitting of Point Vortex Flows