Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions

Abstract We study the simplest parabolic-elliptic model of chemotaxis in space dimensions N ≥ 3 , and show the optimal conditions on the initial data for the finite time blow-up and the global existence of solutions in terms of stationary solutions. Our argument is based on the study of the Cauchy problem for the transformed equation involving the averaged mass of the solution.