Optimal time-decay estimates for a diffusive Oldroyd-B model

作者：Wang, Yinghui^*

来源：Zeitschrift für Angewandte Mathematik und Physik, 2023, 74(1): 3.

DOI：10.1007/s00033-022-01902-w

• Oldroyd-B model
• Optimal decay rate
• Zero viscosity

In this paper, we study the optimal time decay rates for the higher order spatial derivatives of solutions to a diffusive Oldroyd-B model. As pointed out in the Sect. 1.2 of Huang et al. (J Differ Equ 306:456-491, 2022), how to establish the optimal decay estimate for the highest-order spatial derivatives of the solution to this model is still an open problem. Motivated by Wang and Wen (Sci China Math 65:1199-1228, 2022), we give a positive answer to this problem via some delicate analyses on the low- and high-frequency parts of the solution.