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We give a small data global well-posedness result for an incompressibleOldroyd-B model with wave number dissipation in the equation of stress tensor.The result is uniform in solvent Reynolds numbers, and requires only fractionalwave-number dependent dissipation $(-\Delta)^{\beta}$, $\beta \ge \frac{1}{2}$in the added stress.

High Reynolds number and high Weissenberg number Oldroyd-B model with dissipation