Optimal time-decay estimates for an Oldroyd-B model with zero viscosity
arXiv:2111.02059 · doi:10.1016/j.jde.2021.10.046
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.
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])
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