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On the energy equality for very weak solutions to 3D MHD equations

Published online by Cambridge University Press:  18 November 2021

Baishun Lai  and
Yifan Yang
Baishun Lai
Affiliation:
LCSM (MOE) and School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, Hunan, P.R. China (laibaishun@hunnu.edu.cn)
Yifan Yang
Affiliation:
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P.R. China (1263299688@qq.com)
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Abstract

In this paper, we consider the energy equality of the 3D Cauchy problem for the magneto-hydrodynamics (MHD) equations. We show that if a very weak solution of MHD equations belongs to $L^{4}(0,\,T;L^{4}(\mathbb {R}^{3}))$, then it is actually in the Leray–Hopf class and therefore must satisfy the energy equality in the time interval $[0,\,T]$.

Keywords

MHD equationsenergy equalityvery weak solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 6 , December 2022 , pp. 1565 - 1588
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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