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Existence and Time Decay for Global Small Solution of 2D Generalized Magneto-Micropolar Equations

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Abstract

This paper is concerned with the 2D magneto-micropolar equations with linear velocity damping and partial magnetic diffusion. We first examine that this system possesses a unique global smooth solution when the initial data is small. Moreover, we also study on the large-time behavior of these smooth solutions of the system. Under some new observation and rigorous analysis on the structure of the system, we establish the detail \(L^{2}\) decay estimates for solutions and high-order derivatives.

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Acknowledgements

Dong is partially supported by the National Natural Science Foundation of China (No. 11871346), the Natural Science Foundation of Guangdong Province (No. 2018A030313024), NSF of Shenzhen City (No. JCYJ20180305125554234) and Research Fund of Shenzhen University (No. 2017056). Jia was supported by the NNSFC grants No. 11801002 and the NSF of Anhui Province (No. 1808085MA01).

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Authors and Affiliations

  1. Institutes of Physical Science and Information Technology, Anhui University, Hefei, 230601, China

    Yana Guo & Bo-Qing Dong

  2. School of Mathematical Science, Anhui University, Hefei, 230601, China

    Yan Jia

  3. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Bo-Qing Dong

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  1. Yana Guo
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  2. Yan Jia
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  3. Bo-Qing Dong
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Correspondence to Bo-Qing Dong.

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Guo, Y., Jia, Y. & Dong, BQ. Existence and Time Decay for Global Small Solution of 2D Generalized Magneto-Micropolar Equations. Acta Appl Math 174, 3 (2021). https://doi.org/10.1007/s10440-021-00421-6

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