On the dynamics of point vortices with positive intensities collapsing with the boundary - Archive ouverte HAL
Article Dans Une Revue Physica D: Nonlinear Phenomena Année : 2024

On the dynamics of point vortices with positive intensities collapsing with the boundary

Sur la dynamique des point vortex d'intensité positive qui collisionnent au bord

Résumé

In this paper, we study the point-vortex dynamics with positive intensities. We show that in the half-plane and in a disk, collapses of point vortices with the boundary in finite time are impossible, hence the solution of the dynamics is global in time. We also give some necessary conditions for the existence of collapses with the boundary in general smooth bounded domains, in particular, that the trajectory of at least one point vortex has no limit. Some minor results are obtained with unsigned intensities.

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hal-04740808 , version 1 (17-10-2024)

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Martin Donati, Ludovic Godard-Cadillac, Dragoş Iftimie. On the dynamics of point vortices with positive intensities collapsing with the boundary. Physica D: Nonlinear Phenomena, 2024, pp.134402. ⟨10.1016/j.physd.2024.134402⟩. ⟨hal-04740808⟩
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