Regularity Criterion of Weak Solutions to the 3D Incompressible Hall-magnetohydrodynamic Equations

LIU Kun-hong, YUAN Bao-quan

doi:10.13371/j.cnki.chin.q.j.m.2015.03.004

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 3: 339 - 348

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.03.004

Regularity Criterion of Weak Solutions to the 3D Incompressible Hall-magnetohydrodynamic Equations

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School of Mathematics and Information Science, Henan Polytechnic University

LIU Kun-hong(1989-), female, native of Shangqiu, Henan, graduate student; YUAN Bao-quan(1965-), male, native of Jiaozuo, Henan, a professor of Henan Polytechnic University, Ph.D., engages in partial differential equations and applications.

Received date: 2015-02-16

Online published: 2020-11-20

Supported by

Supported by the National Natural Science Foundation of China(11471103)；

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Abstract

In this paper,we study the regularity criterion of weak solutions to the3 D incompressible Hall-magnetohydrodynamics,which is ifu and Bsatisfy the condition∫₀^T‖\alpha_x3u（t）‖^q_LP+‖▽B‖γLβdt<∞ with 3/p+2/q≤1,3/β+2/γ≤1,p>3,β>3,then the weak solution（u,B） is a smooth one on(0,T].

Key words： incompressible Hall-magnetohydrodynamic equations; regularity criterion; weak solutions

Cite this article

LIU Kun-hong, YUAN Bao-quan . Regularity Criterion of Weak Solutions to the 3D Incompressible Hall-magnetohydrodynamic Equations[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(3) : 339 -348 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.03.004

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