Article contents
On the energy equality for very weak solutions to 3D MHD equations
Published online by Cambridge University Press: 18 November 2021
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 $[0,\,T]$.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 6 , December 2022 , pp. 1565 - 1588
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
References
- 1
- Cited by