The purpose of this paper is to study the global wellposedness and large time behavior results of strong solutions for the compressible Oldroyd-B model derived by Barrett, Lu, Süli (Commun. Math. Sci., 15, 1265–1323, 2017). Exploiting the harmonic analysis tools (especially Littlewood-Paley theory), we first study the global well-posedness of the model with small initial data in spaces with low regularity. Then, under some suitable conditions involving only the low frequency of the initial data, we also obtain the optimal decay rates of the solutions. Compared with the result by Wang and Wen (Math. Models Methods Appl. Sci., 30, 139–179, 2020), the polymer number density is allowed to vanish and the stress tensor is near zero equilibrium.

本文的目的是研究Barrett，Lu，Süli（Commun。Math。Sci。，15，1265–1323，2017）导出的可压缩Oldroyd-B模型强解的全局适定性和长时间行为结果。利用谐波分析工具（尤其是Littlewood-Paley理论），我们首先研究了在规则性较低的空间中具有少量初始数据的模型的整体适定性。然后，在一些仅涉及初始数据低频的合适条件下，我们还获得了解的最优衰减率。与Wang和Wen（Math。Models Methods Appl。Sci。，30，139–179，2020）的结果相比，允许聚合物数密度消失，应力张量接近零平衡。