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Consider a global wellposed problem for the incompressible Oldroyd-B model.It is shown that this set of equations admits a unique global solution providedthe initial horizontal velocity $u^h_0$, the product $\om u^d_0$ of thecoupling parameter $\om$ and initial the vertical velocity $u^d_0$, and initialsymmetric tensor of constrains $\tau_0$ are sufficient small in the scalinginvariant Besov space$\dot{B}^{\fr{d}{2}-1}_{2,1}\times\dot{B}^{\fr{d}{2}}_{2,1}, d\ge2$. Inparticular, the result implies the global well-posedness of Oldroyd-B modelwith large initial vertical velocity $u_0^d$.

Global solutions to the Oldroyd-B model with a class of large initial data