数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (1): 237-244.doi: 10.1007/s10473-020-0116-x

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THE ENERGY CONSERVATIONS AND LOWER BOUNDS FOR POSSIBLE SINGULAR SOLUTIONS TO THE 3D INCOMPRESSIBLE MHD EQUATIONS

Jae-Myoung KIM   

  1. Department of Mathematics Education Andong National University, Andong, Republic of Korea
  • 收稿日期:2018-09-27 修回日期:2019-03-04 出版日期:2020-02-25 发布日期:2020-04-14
  • 基金资助:
    This work was supported by a Research Grant of Andong National University NRF-2015R1A5A1009350 and NRF-2016R1D1A1B03930422.

THE ENERGY CONSERVATIONS AND LOWER BOUNDS FOR POSSIBLE SINGULAR SOLUTIONS TO THE 3D INCOMPRESSIBLE MHD EQUATIONS

Jae-Myoung KIM   

  1. Department of Mathematics Education Andong National University, Andong, Republic of Korea
  • Received:2018-09-27 Revised:2019-03-04 Online:2020-02-25 Published:2020-04-14
  • Supported by:
    This work was supported by a Research Grant of Andong National University NRF-2015R1A5A1009350 and NRF-2016R1D1A1B03930422.

摘要: In this note, we give a new proof to the energy conservation for the weak solutions of the incompressible 3D MHD equations. Moreover, we give the lower bounds for possible singular solutions to the incompressible 3D MHD equations.

关键词: MHD equation, lower bounds, incompressible

Abstract: In this note, we give a new proof to the energy conservation for the weak solutions of the incompressible 3D MHD equations. Moreover, we give the lower bounds for possible singular solutions to the incompressible 3D MHD equations.

Key words: MHD equation, lower bounds, incompressible

中图分类号: 

  • 35Q35