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Remarks on uniqueness and energy conservation for electron-MHD system

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Abstract

This paper is concerned with the uniqueness and energy conservation of weak solutions for Electron-MHD system. Under suitable assumptions, we first show that the Electron-MHD system has a unique weak solution. In addition, we show that weak solution conserves energy if \(\nabla \times b\in L^2(0, T; L^4({\mathbb {R}}^d))(d\ge 2)\) or \( \nabla \times b \in L^{\frac{4d+8}{d+4}}\left( 0, T; L^{\frac{4d+8}{d+4}}({\mathbb {R}}^{d})\right) (d=2, 3, 4)\).

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Acknowledgements

The author is indebted to the referee for careful reading of the paper and helpful suggestions, and would like to express his sincere gratitude to Dr. Zhengmao Chen for many helpful discussions and suggestions. F. Wu was supported by Jiangxi Provincial Natural Science Foundation (20224BAB211003), the Science and Technology Project of Jiangxi Provincial Department of Education (GJJ2201524) and the doctoral research start-up project of Nanchang Institute of Technology (2022kyqd044).

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  1. College of Science, Nanchang Institute of Technology, Key Laboratory of Engineering Mathematics and Advanced Computingn of Nanchang Institute of Technology, Nanchang, 330099, Jiangxi, China

    Fan Wu

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Wu, F. Remarks on uniqueness and energy conservation for electron-MHD system. J. Evol. Equ. 24, 24 (2024). https://doi.org/10.1007/s00028-024-00955-w

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