We consider an Oldroyd-B model which is derived in Ref. 4 [J. W. Barrett, Y. Lu and E. Süli, Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model, Commun. Math. Sci. 15 (2017) 1265–1323] via micro–macro-analysis of the compressible Navier–Stokes–Fokker–Planck system. The global well posedness of strong solutions as well as the associated time-decay estimates in Sobolev spaces for the Cauchy problem are established near an equilibrium state. The terms related to [Formula: see text], in the equation for the extra stress tensor and in the momentum equation, lead to new technical difficulties, such as deducing [Formula: see text]-norm dissipative estimates for the polymer number density and its spatial derivatives. One of the main objectives of this paper is to develop a way to capture these dissipative estimates via a low–medium–high-frequency decomposition.

中文翻译：

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Oldroyd-B 模型在三个维度上的柯西问题

我们考虑在参考文献中派生的 Oldroyd-B 模型。4 [JW Barrett、Y. Lu 和 E. Süli，可压缩 Oldroyd-B 模型的大数据有限能量全局弱解的存在，Commun。数学。科学。15 (2017) 1265-1323] 通过可压缩 Navier-Stokes-Fokker-Planck 系统的微观宏观分析。柯西问题的强解的全局适定性以及索博列夫空间中相关的时间衰减估计是在平衡状态附近建立的。在额外应力张量方程和动量方程中与[公式：见文本]相关的术语导致了新的技术难题，例如推导聚合物数密度的[公式：见文本]-范数耗散估计和其空间导数。