Optimal Decay Rates of Solutions to a Blood Flow Model

Abstract

In this paper, we are concerned with the asymptotic behavior of solutions to Cauchy problem of a blood flow model. Under some smallness conditions on the initial perturbations, we prove that Cauchy problem of blood flow model admits a unique global smooth solution, and such solution converges time-asymptotically to corresponding equilibrium states. Furthermore, the optimal convergence rates are also obtained. The approach adopted in this paper is Green’s function method together with time-weighted energy estimates.