Remarks on uniqueness and energy conservation for electron-MHD system

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