Optimal time-decay rate of global classical solutions to the generalized compressible Oldroyd-B model

In this paper, we investigate the optimal time-decay rates of global classical solutions for the compressible Oldroyd-B model in \begin{document}$ \mathbb{R}^n(n = 2,3) $\end{document} . Global classical solutions in two space dimensions are still open. We first complete the proof of global classical solutions in two space dimensions. Based on global classical solutions and Fourier spectrum analysis, we obtain the optimal time-decay rates of global classical solutions in two and three space dimensions. More precisely, if the initial data belong to \begin{document}$ L^1 $\end{document} , the optimal time-decay rate of solutions and time-decay rates of \begin{document}$ l(l = 1,\cdot\cdot\cdot,m) $\end{document} order derivatives under additional assumptions are established.