Global existence of weak solutions to a parabolic attraction-repulsion chemotaxis model in R3: The repulsive dominant case

Abstract

We consider the Cauchy problem for a full parabolic attraction-repulsion chemotaxis model in three dimensions. Due to the combination of diffusion, aggregation and repulsion effects, solutions to the model may exist globally or blow up in finite time. It is natural to expect that solutions exist globally in time when the chemorepellent is dominant. However, the global existence is only known in two dimensions. In this work, we establish the global existence of weak solutions for the repulsive dominant case in three dimensions.