Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model. (15th December 2013) - Xie, Weijun; Zhang, Yinghui; Xiao, Yuandong; Wei, Wei
Abstract : 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 by combining spectral analysis with energy methods.