The large-time behavior of the multi-dimensional hyperbolic-parabolic model arising from chemotaxis

Abstract

The present paper is dedicated to the study of large-time behavior of global strong solutions to the initial value problem for the hyperbolic-parabolic system derived from chemotaxis models in any dimension d ≥ 2. Under a suitable additional decay assumption involving only the low frequencies of the data and in L2-critical regularity framework, we exhibit the decay rates of strong solutions to the system for initial data close to a stable equilibrium state. The proof relies on a refined time-weighted energy functional in the Fourier space and the Littlewood-Paley decomposition technology.The present paper is dedicated to the study of large-time behavior of global strong solutions to the initial value problem for the hyperbolic-parabolic system derived from chemotaxis models in any dimension d ≥ 2. Under a suitable additional decay assumption involving only the low frequencies of the data and in L2-critical regularity framework, we exhibit the decay rates of strong solutions to the system for initial data close to a stable equilibrium state. The proof relies on a refined time-weighted energy functional in the Fourier space and the Littlewood-Paley decomposition technology.