LAUSR

Abstract We consider the Cauchy problem for an attraction–repulsion chemotaxis system in R 2 with the chemotactic coefficient of the attractant β 1 and that of the repellent β 2 . It is known that in the repulsive dominant case β 1 β 2 or the balance case β 1 = β 2 , the nonnegative solutions to the Cauchy problem exist globally in time, whereas in the attractive dominant case β 1 > β 2 , there are blowing-up solutions in finite time under the assumption ( β 1 − β 2 ) ∫ R 2 u 0 d x > 8 π on the nonnegative initial data u 0 . In this paper, we show the global existence of nonnegative solutions to the Cauchy problem under the assumption ( β 1 − β 2 ) ∫ R 2 u 0 d x 8 π in the attractive dominant case.