High Reynolds number and high Weissenberg number Oldroyd-B model with dissipation

Constantin, Peter; Wu, Jiahong; Zhao, Jiefeng; Zhu, Yi

doi:10.48550/arxiv.2001.03703

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2021

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“…As showed by Málek et al ([43]), the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism. Thus the diffusive Oldroyd-B system has attracted much attention and been studied extensively, see [1,2,12,13,14,18,19,33,42,49].…”

Section: Introductionmentioning

confidence: 99%

Optimal time-decay estimates for an Oldroyd-B model with zero viscosity

Huang

Wang

Wen

et al. 2021

Preprint

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In this work, we consider the Cauchy problem for a diffusive Oldroyd-B model in three dimensions. Some optimal time-decay rates of the solutions are derived via analysis of upper and lower time-decay estimates provided that the initial data are small and that the absolute value of Fourier transform of the initial velocity is bounded below away from zero in a low-frequency region. It is worth noticing that the optimal rates are independent of the fluid viscosity or the diffusive coefficient, which is a different phenomenon from that for incompressible Navier-Stokes equations.

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