We are concerned with a 3D chemotaxis model arising from biology, which is a coupled hyperbolic-parabolic system. We prove the global existence of a strong solution when H~2-norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally, L~1-norm of the initial perturbation is bounded; the optimal convergence rates are also obtained for such a solution. The proofs are obtained b...
