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In this work, we consider the Cauchy problem for a diffusive Oldroyd-B modelin three dimensions. Some optimal time-decay rates of the solutions are derivedvia analysis of upper and lower time-decay estimates provided that the initialdata are small and that the absolute value of Fourier transform of the initialvelocity is bounded below away from zero in a low-frequency region. It is worthnoticing that the optimal rates are independent of the fluid viscosity or thediffusive coefficient, which is a different phenomenon from that forincompressible Navier-Stokes equations.

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