Global regularity for the 2D Oldroyd-B model in the corotational case.

This paper is dedicated to the Oldroyd-B model with fractional dissipation (−Δ) α τ for any α > 0. We establish the global smooth solutions to the Oldroyd-B model in the corotational case with arbitrarily small fractional powers of the Laplacian in two spatial dimensions. Moreover, in the Appendix, we provide some a priori estimates to the Oldroyd-B model in the critical case, which may be useful and of interest for future improvement. Therefore, our result is closer to the resolution of the well-known global regularity issue on the critical 2D Oldroyd-B model. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]