Global Existence and Convergence Rates for the Strong Solutions inH2to the 3D Chemotaxis Model

[摘要] 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 whenH2-norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally,L1-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.

[学科分类] 应用数学