Abstract
In this paper, we derive an incompressible Oldroyd-B model with hybrid dissipation and partial damping on stress tensor \(\tau \) via the velocity equations and the generalized constitutive law so that global well-posedness of the model is established in the Sobolev space framework. Precisely speaking, the proof is based on the curl-div free property of \(\tau - {\nabla }\frac{1}{\Delta } \mathbb {P}\mathrm{div}\tau - ( {\nabla } \frac{1}{\Delta } \mathbb {P}\mathrm{div}\tau )^T \), the low frequency dissipation and high frequency damping of \(\tau \) and the dissipation of u.
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The authors would like to thank the reviewers for their valuable comments and suggestions, which helped improve its presentation overall.
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This work is supported by the National Natural Science Foundation of China (Grant No. 11871452).
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Deng, C., He, Q. & Yan, D. Global Solutions to the 2-Dimensional Incompressible Oldroyd-B Model with Hybrid Dissipation and Partial Damping on Stress Tensor. Results Math 76, 18 (2021). https://doi.org/10.1007/s00025-020-01331-z
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DOI: https://doi.org/10.1007/s00025-020-01331-z