Optimal time-decay estimates for an Oldroyd-B model with zero viscosity
Abstract
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.
Cite
@article{arxiv.2111.02059,
title = {Optimal time-decay estimates for an Oldroyd-B model with zero viscosity},
author = {Jinrui Huang and Yinghui Wang and Huanyao Wen and Ruizhao Zi},
journal= {arXiv preprint arXiv:2111.02059},
year = {2026}
}
Comments
A revised version of [J. Differential Equations, 306(2022), 456-491]. This revised version updates Theorem 1.2, adds a new remark (Remark 1.6), and includes an additional reference ([49])