Vortex collapses for the Euler and Quasi-Geostrophic models

<p style='text-indent:20px;'>This article studies point-vortex models for the Euler and surface quasi-geostrophic equations. In case of an inviscid fluid with planar motion, model gives account dynamics where vorticity profile is sharply concentrated around some points approximated by Dirac masses. This contains two main theorems also smaller propositions several links between each other. The first result focuses on model, under non-neutral cluster hypothesis we prove a convergence result. second devoted to generalization classical Marchioro Pulvirenti concerning improbability collapses extension this case.</p>