Global Existence For A Nonlocal Multi-Species Aggregation-Diffusion Equation

Abstract

We consider the question of global existence of smooth solutions to a multi-species aggregation-diffusion equation for a class of singular interaction kernels. We establish a smallness condition on the initial data which yields global existence of smooth solutions. We also give conditions on the species interaction which ensure that pointwise inequalities comparing species densities are preserved by the evolution.

substantial revisions, new existence theorem added, typos corrected, many references added