Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (3): 339-348.doi: 10.13371/j.cnki.chin.q.j.m.2015.03.004

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

  

  1. School of Mathematics and Information Science, Henan Polytechnic University
  • Received:2015-02-16 Online:2015-09-30 Published:2020-11-20
  • About author: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.
  • Supported by:
    Supported by the National Natural Science Foundation of China(11471103);

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∫0T\alphax3u(t)‖qLP+‖▽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

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