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

TL;DR

This paper proves global existence and decay rates for solutions to the Oldroyd-B model in multiple dimensions, using simplified methods and minimal initial data assumptions, highlighting the system's structural properties.

Contribution

It provides a simplified proof of global well-posedness and establishes optimal decay rates for the Oldroyd-B model with minimal initial data restrictions.

Findings

Global existence of solutions for small initial data in critical Besov spaces.

Optimal decay rates of solutions under minimal assumptions.

Utilization of velocity dissipation and damping mechanisms.

Abstract

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.