Global regularity for Oldroyd-B model with only stress tensor dissipation

Article type: Research Article

Authors: Feng, Weixun^a | Chen, Zhi^{b; *} | Qin, Dongdong^a | Tang, Xianhua^a

Affiliations: [a] School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, 410083 Hunan, P. R. China | [b] School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002 Anhui, P. R. China

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: 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.

Keywords: Oldroyd-B model, tensor dissipation, global solutions, time independent bound

DOI: 10.3233/ASY-231861

Journal: Asymptotic Analysis, vol. 135, no. 3-4, pp. 445-461, 2023