Suppression of blow-up of solutions for the Cauchy problem of a generalized Keller-Segel model via the Couette flow

In this paper, we use the Green's function method to prove the dissipative enhancement effect of the Couette flow combined with a diffusion term. We further prove that this dissipative enhancement can suppress the blow-up of solutions for a kind of generalized attraction chemotaxis model, and obtain the globe existence and decaying estimates for the Cauchy problem. We also try to explore a generalized framework about how to use the enhanced dissipation induced by shear flows to suppress the blasting of solutions under large initial perturbations, and how to obtain the global existence and decaying estimates by using the Green's function method in a setting of large initial perturbations.