On the global existence and time-decay rates for a parabolic–hyperbolic model arising from chemotaxis

Abstract

In this paper, we are concerned with the study of the Cauchy problem for a parabolic–hyperbolic model arising from chemotaxis in any dimension [Formula: see text]. We first prove the global existence of the model in [Formula: see text] critical regularity framework with respect to the scaling of the associated equations. Furthermore, under a mild additional decay assumption involving only the low frequencies of the data, we also establish the time-decay rates for the constructed global solutions. Our analyses mainly rely on Fourier frequency localization technology and on a refined time-weighted energy inequalities in different frequency regimes.