In this paper, inspired by the work of Chen–Liang–Wang–Xu (Chen et al., 2020) on compressible Navier–Stokes equations, we obtain the energy conservation for weak solutions of the compressible non-resistive magnetohydrodynamic flows in a bounded domain $\Omega \subset {\mathbb{R}}^3$. To ensure the energy conservation, we need the same regularity conditions of density and velocity as in Chen et al. (2020), moreover, $\mathbf{H}\in L_t^4{L}_x^4$ and $\nabla \mathbf{H}\in L_t^{p_1}{L}_x^{q_1}$, where $p_1=\frac{4p}{3p-4}$, $q_1=\frac{4q}{3q-4}$. Under these conditions, $p_1\in (\frac{4}{3},2]$, $q_1\in (\frac{4}{3},\frac{12}{7}]$ when $p\ge 4$ and $q\ge 6$.

中文翻译：

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有界域中粘性非电阻流体的 3D 可压缩磁流体动力学方程弱解的能量守恒

在本文中，受到 Chen-Liang-Wang-Xu (Chen et al., 2020) 关于可压缩 Navier-Stokes 方程的工作的启发，我们获得了有界可压缩非电阻磁流体动力流动弱解的能量守恒领域 $\Omega \subset {\mathbb{电阻}}^3$. 为了确保能量守恒，我们需要与 Chen 等人相同的密度和速度的规律性条件。(2020) 此外，$\mathbf{H}\in {升}_{吨}^4{升}_X^4$ 和 $\nabla \mathbf{H}\in {升}_{吨}^{{磷}_{\mathrm{1个}}}{升}_X^{q_{\mathrm{1个}}}$， 在哪里 ${磷}_{\mathrm{1个}}=\frac{4磷}{3磷-4}$, $q_{\mathrm{1个}}=\frac{4q}{3q-4}$. 在这些条件下，${磷}_{\mathrm{1个}}\in (\frac{4}{3},2]$, $q_{\mathrm{1个}}\in (\frac{4}{3},\frac{12}{7}]$ 什么时候 $磷\ge 4$ 和 $q\ge 6$.