Global Boundedness Of Solutions To A Keller-Segel System With Double Cross-diffusion

In this paper,we study the Keller-Segel system where Ω(?)RN(N≥ 2)is a bounded domain with smooth boundary.It is obtained that if ∫ΩUN/2(·,t)is bounded,and{∫N/2-(·,t)|t∈(0.Tmax)} is equi-integrable,then the solutions are globally bounded.The parallel result was established by Cao Xinru[An interpolation inequality and its application in Keller-Segel model]for the classical chemotaxis model of Keller-Segel system.