The optimal time decay rates for the compressible Oldroyd-B model in ℝ3

Abstract

In this paper, we consider the optimal time decay rates of the higher order spatial derivatives of global solution for the three-dimensional compressible Oldroyd-B model, which was derived independently by Barrett-Lu-Süli [Commun. Math. Sci., 15(5): 1265–1323, 2017] via micro–macro analysis of the compressible Navier–Stokes–Fokker–Planck system. We show that under H 3 framework, the third-order spatial derivatives of global small solution of the compressible Oldroyd-B model decay at the rate ( 1 + t ) − 9 4 instead of ( 1 + t ) − 7 4 stated by Wang-Wen [Math. Models Methods Appl. Sci., 30(1): 139–179, 2020]. This decay rate is optimal in the sense that it coincides with that of solutions to heat equation.