Hölder estimate for the 3 point-vortex problem with alpha-models

Abstract

In this article we study quasi-geostrophic point-vortex systems in a general setting called alpha point-vortex. We study a particular case of vortex collapses called mono-scale collapses and this study gives the Hölder regularity for the $3$-vortex problem. This result implies in particular that the trajectories of the vortices are convergent even in the case of a collapse.