Reference : Burst of Point Vortices and Non-Uniqueness of 2D Euler Equations
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Burst of Point Vortices and Non-Uniqueness of 2D Euler Equations
Grotto, Francesco mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Pappalettera, Umberto mailto []
[en] Point vortex ; 2d Euler equations
[en] 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.

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