Global Existence and Boundedness of a Chemotaxis System with Logistic Source

In this paper, we mainly study Neumann initial-boundary value problems for the chemotaxis system with logistic source in three-dimensional bounded domain. By using the inequality technique, the expression of the solutions and the semigroup theory, etc, we proved that for logistic source term, when the nonlinear growth index α > 7/3, this Neumann boundary-value problem possesses a unique global bounded classical solution.