Global Well-Posedness in the Critical Besov Spaces for the Incompressible Oldroyd-B Model Without Damping Mechanism

We prove the global well-posedness in the critical Besov spaces for the incompressible Oldroyd-B model without damping mechanism on the stress tensor in R d for the small initial data. Our proof is based on the observation that the behaviors of Green’s matrix to the system of ( u , ( - Δ ) - 1 2 P ∇ · τ ) as well as the effects of τ change from the low frequencies to the high frequencies and the construction of the appropriate energies in different frequencies.