In this paper, we consider the d-dimensional (d⩾2) Oldroyd-B model with only dissipation in the equation of stress tensor, and establish a small data global well-posedness result in critical Lp framework. Particularly, we give a positive answer to the problem proposed recently by Wu-Zhao (J. Differ. Equ. 316 (2022)) involving the upper bound for the time integral of the lower frequency piece of the stress tensor, and show that it is indeed independent of the time. Moreover, we improve the results in (J. Math. Fluid Mech. 24 (2022)) by relaxing the space dimension d=2,3 to any d⩾2.

中文翻译：

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仅具有应力张量耗散的 Oldroyd-B 模型的全局正则性

本文考虑应力张量方程中仅有耗散的d维(d⩾2)Oldroyd-B模型，并在临界Lp框架下建立小数据全局适定性结果。特别是，我们对 Wu-Zhao (J. Differ. Equ. 316 (2022)) 最近提出的涉及应力张量低频部分时间积分上限的问题给出了肯定的答案，并表明确实与时间无关。此外，我们通过将空间维度 d=2,3 放宽到任意 d⩾2 来改进 (J. Math. Fluid Mech. 24 (2022)) 中的结果。