Confinement for repulsive-attractive kernels

Abstract

We investigate the confinement properties of solutions of theaggregation equation with repulsive-attractive potentials. We showthat solutions remain compactly supported in a large fixed balldepending on the initial data and the potential. The argumentsapply to the functional setting of probability measures withmildly singular repulsive-attractive potentials and to thefunctional setting of smooth solutions with a potential being thesum of the Newtonian repulsion at the origin and a smooth suitablygrowing at infinity attractive potential.