Global well-posedness and large time behavior for the Oldroyd-B model

This paper studies the global well-posedness and optimal decay estimates to the Oldroyd-B model in $\mathbb R^d$ ($d\geq2$). By utilizing the special structure of this system, we give a simplified proof to the global existence of solutions for the case of initial data small in critical Besov spaces and non-small coupling parameters. Moreover, the optimal decay rates of the solutions under minimal small assumption on the initial data are established by fully making use of the effect of velocity dissipation and damping mechanism.