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Global Regularity for the Incompressible Oldroyd-B Model with Only Stress Tensor Dissipation in Critical \({{\varvec{L}}}^{{{\varvec{p}}}}\) Framework

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Abstract

This work is concerned with the global solutions to the d-dimensional incompressible Oldroyd-B model with only dissipation in the equation of stress tensor (without stress tensor damping or velocity dissipation). The main ingredients of the proof lies in commutator estimate at low frequency and energy estimate in Lagrangian coordinates at high frequency. Particularly, our result extends the works of Wu–Zhao [24] (J. Differ. Equ. 316, 2021) and Constantin–Wu–Zhao–Zhu [9] (J. Evol. Equ. 21, 2021).

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Acknowledgements

This work is partially supported by China Scholarship Council (Nos.202006370255) and the National Natural Science Foundation of China (Nos. 11801574, 11971485, 12171486, 12161091), Natural Science Foundation of Hunan Province (No. 2019JJ50788), Central South University Innovation-Driven Project for Young Scholars (No. 2019CX022) and Fundamental Research Funds for the Central Universities of Central South University, China (Nos. 2020zzts038, 2021zzts0041).

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Authors and Affiliations

  1. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, , 410083, Hunan, People’s Republic of China

    Zhi Chen & Dongdong Qin

  2. School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241002, Anhui, People’s Republic of China

    Lvqiao Liu

  3. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, , Beijing, 100088, People’s Republic of China

    Weikui Ye

  4. Dipartimento di Matematica, Università di Milano, Via C. Saldini 50, 20133, Milan, Italy

    Zhi Chen

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  1. Zhi Chen
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  2. Lvqiao Liu
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  3. Dongdong Qin
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Correspondence to Lvqiao Liu.

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Communicated by L. Székelyhidi.

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Chen, Z., Liu, L., Qin, D. et al. Global Regularity for the Incompressible Oldroyd-B Model with Only Stress Tensor Dissipation in Critical \({{\varvec{L}}}^{{{\varvec{p}}}}\) Framework. J. Math. Fluid Mech. 24, 54 (2022). https://doi.org/10.1007/s00021-022-00675-6

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