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 \( \nabla \times b \in L^{\frac{4d+8}{d+4}}\left( 0, T; L^{\frac{4d+8}{d+4}}({\mathbb {R}}^{d})\right) (d=2, 3, 4)\).

中文翻译：

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电子磁流体动力学系统的独特性和节能性评述

本文主要研究电子磁流体动力学系统弱解的唯一性和能量守恒性。在适当的假设下，我们首先证明电子 MHD 系统具有唯一的弱解。此外，我们还证明，如果\(\nabla \times b\in L^2(0, T; L^4({\mathbb {R}}^d))(d\ge 2)\ )或\( \nabla \times b \in L^{\frac{4d+8}{d+4}}\left( 0, T; L^{\frac{4d+8}{d+4}} ({\mathbb {R}}^{d})\right) (d=2, 3, 4)\)。