Global Existence and Convergence Rates for the Strong Solutions in H2 to the 3D Chemotaxis Model

Abstract EN

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 H2-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.