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A regularity criterion for three-dimensional micropolar fluid equations in Besov spaces of negative regular indices

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Abstract

In this article, we study regularity criteria for the 3D micropolar fluid equations in terms of one partial derivative of the velocity. It is proved that if

$$\begin{aligned} \int ^{T}_{0}\Vert \partial _{3}u\Vert ^{\frac{2}{1-r}}_{\dot{B}^{-r}_{\infty ,\infty }} dt<\infty \quad \text {with} \quad 0< r<1, \end{aligned}$$

then, the solutions of the micropolar fluid equations actually are smooth on (0, T). This improves and extends many previous results.

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Acknowledgements

The first author is partially supported by I.N.D.A.M-G.N.A.M.P.A. 2019 and the “RUDN University Program 5-100”.

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Authors and Affiliations

  1. Department of Mathematics, University of Catania, Viale Andrea Doria No. 6, 95128, Catania, Italy

    Maria Alessandra Ragusa

  2. RUDN University, 6 Miklukho -Maklay St, Moscow, Russia, 117198

    Maria Alessandra Ragusa

  3. School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, China

    Fan Wu

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  1. Maria Alessandra Ragusa
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Correspondence to Maria Alessandra Ragusa.

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Ragusa, M.A., Wu, F. A regularity criterion for three-dimensional micropolar fluid equations in Besov spaces of negative regular indices. Anal.Math.Phys. 10, 30 (2020). https://doi.org/10.1007/s13324-020-00370-7

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  • DOI: https://doi.org/10.1007/s13324-020-00370-7

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