Local well-posedness and finite time blow-up of solutions to an attraction–repulsion chemotaxis system in higher dimensions

Abstract

We consider the Cauchy problem for an attraction–repulsion chemotaxis system in Rn with the chemotactic coefficients of the attractant β1 and the repellent β2. In particular, these coefficients are important role in the global existence and blow up of the solutions. In this paper, we show the local well-posedness of solutions in the critical spaces Ln/2(Rn) and the finite time blow-up of the solution under the condition β1>β2 in higher dimensional spaces.