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 -norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally, -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.
"Global Existence and Convergence Rates for the Strong Solutions in to the 3D Chemotaxis Model." J. Appl. Math. 2013 1 - 9, 2013. https://doi.org/10.1155/2013/391056