A Regularity Criterion Via the Pressure On the Three-dimensional Micropolar Fluid Equations in Besov Space

LIU Jiang-jun, QU Zhen, HU Gang

doi:10.13371/j.cnki.chin.q.j.m.2020.01.004

Chinese Quarterly Journal of Mathematics >

2020 , Vol. 35 >Issue 1: 46 - 55

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.01.004

A Regularity Criterion Via the Pressure On the Three-dimensional Micropolar Fluid Equations in Besov Space

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1.Huanghe Jiaotong University, Henan, 454000, China;
2.Faculty of Sciences Xian University of Tech¬nology, Xian 710054, China

LIU Jiang-jun(1981-), male, native of Zhonzhi, Shanxi, instructor, engages in partial dif¬ferential equations and applications; QU Zhen(1982-), male, native of Xiaxian, Henan, instructor, engages in computational mathematics; HU Gang (1979-), male, native of Gaian, Jiangxi, professor, engages in computa¬tional geometry

Received date: 2020-10-30

Online published: 2020-08-06

Supported by

Supported by the National Natural Science Foundation of China(NO.51305344)

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Abstract

In this paper, we investigate the regularity criterion via the pressure of weak solutions to the micropolar fluid equations in three dimensions. We obtain that for 0 < a < 1 if $p \epsilon L^{\frac{2}{\alpha}} (0,T, \dot{B}_{\infty, \infty}^{\alpha})$, then the weak solution (υ,ω) is regular on (0, T].

Key words： micropolar fluid equations; pressure; regularity criteria; Besov space

Cite this article

LIU Jiang-jun, QU Zhen, HU Gang . A Regularity Criterion Via the Pressure On the Three-dimensional Micropolar Fluid Equations in Besov Space[J]. Chinese Quarterly Journal of Mathematics, 2020 , 35(1) : 46 -55 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.01.004

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