Global regularity for the 2D Oldroyd‐B model in the corotational case |
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Authors: | Zhuan Ye Xiaojing Xu |
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Affiliation: | 1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, China;2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems,Ministry of Education, Beijing 100875, People's Republic of China |
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Abstract: | This paper is dedicated to the Oldroyd‐B model with fractional dissipation (?Δ)ατ 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. |
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Keywords: | Oldroyd‐B model fractional dissipation global smooth solutions subclass76A10 76D03 76A05 76N99 |
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