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

摘要

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 Rd for the small initial data. Our proof is based on the observation that the behaviors of Green's matrix to the system of (u,(-Delta)-P del tau) as well as the effects of tau change from the low frequencies to the high frequencies and the construction of the appropriate energies in different frequencies.