Regularity Criterion of Weak Solutions to the 3D Micropolar Fluid Equations in Besov Space

LI Xiao

doi:10.13371/j.cnki.chin.q.j.m.2020.04.010

Chinese Quarterly Journal of Mathematics >

2020 , Vol. 35 >Issue 4: 418 - 423

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.04.010

Regularity Criterion of Weak Solutions to the 3D Micropolar Fluid Equations in Besov Space

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Department of Mathematics Teaching and Research, Huanghe Jiaotong University, Henan, 454000,
China

LI Xiao(1991-), femal, native of Fanxian, Henan, graduate student, engages in partial differential equations and applications.

Received date: 2020-04-10

Online published: 2021-01-06

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Abstract

This paper studies the regularity criterion of weak solutions to the micropolar
fluid equations in three dimensions. Let (∇u∈L ^{2/ 2- γ} (0,T; ˙B^{- γ}_∞,∞),∇ω ∈L²(0,T; ˙B^-1 _∞,∞), it
is showed that the weak solution (u,ω) is globally regular for the case 0< γ <2.

Key words： Micropolar fluid equations; Regularity criteria; Besov space

Cite this article

LI Xiao . Regularity Criterion of Weak Solutions to the 3D Micropolar Fluid Equations in Besov Space[J]. Chinese Quarterly Journal of Mathematics, 2020 , 35(4) : 418 -423 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.010

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