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

In this paper, we consider the optimal time decay rates of the higher order spatial derivatives of global solution for the three-dimensional compress-ible Oldroyd-B model, which was derived independently by Barrett-Lu-Suli [Commun. Math. Sci., 15(5): 1265-1323, 2017] via micro-macro analysis of the compressible Navier-Stokes-Fokker-Planck system. We show that under H3 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.