D. Balagué, J. A. Carrillo, Y. Yao


We investigate the confinement properties of solutions of the aggregation equation with repulsive-attractive potentials. We show that solutions remain compactly supported in a large fixed ball depending on the initial data and the potential. The arguments apply to the functional setting of probability measures with mildly singular repulsive-attractive potentials and to the functional setting of smooth solutions with a potential being the sum of the Newtonian repulsion at the origin and a smooth suitably growing at infinity attractive potential.

Discrete and Continuous Dynamical Systems-B 19, 1227–1248, 2014.

arXiv Mon, 1 Oct 2012