Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (3): 865-871.doi: 10.1016/S0252-9602(13)60046-6

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ENERGY DISSIPATION FOR WEAK SOLUTIONS OF INCOMPRESSIBLE MHD EQUATIONS

 GAO Zhen-Sheng, TAN Zhong*, WU Guo-Chun   

  1. School of Mathematical Sciences, Huaqiao University, Fujian 362021, China;
    ScSchool of Mathematical Sciences, Xiamen University, Fujian 361005, China
  • Received:2012-02-27 Revised:2012-06-30 Online:2013-05-20 Published:2013-05-20
  • Contact: TAN Zhong,ztan85@163.com E-mail:gaozhensheng@hqu.edu.cn;ztan85@163.com; guochunwu@126.com
  • Supported by:

    Supported by NSFC (10976026), and the first author is also supported by the Fundamental Research Funds for the Central Universities (11QZR18) and the Research Funds for high-level talents of Huaqiao University (12BS232).

Abstract:

In this article, we mainly study the local equation of energy for weak solutions of 3D MHD equations. We define a dissipation term D(u,B) that stems from an eventual lack of smoothness in the solution, and then obtain a local equation of energy for weak solutions of 3D MHD equations. Finally, we consider the 2D case at the end of this article.

Key words: Energy dissipation, incompressible, MHD equations

CLC Number: 

  • 35Q35
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