In this paper, we prove the energy conservation for the weak solutions of the three-dimensional ideal inhomogeneous magnetohydrodynamic (MHD) equations in a bounded domain. Two types of sufficient conditions on the regularity of the weak solutions are provided to ensure the energy conservation. Due to the presence of the boundary, we need to impose the boundedness in $L^p$ and the continuity in $L^{\frac{p}{p-2}}$ for the velocity and magnetic fields near the boundary.

中文翻译：

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有界域中理想非齐次磁流体动力学方程弱解的能量守恒

在本文中，我们证明了有界域中三维理想非齐次磁流体动力学（MHD）方程弱解的能量守恒。为保证能量守恒，给出弱解的正则性的两类充分条件。由于边界的存在，我们需要在${升}^{磷}$ 和连续性 ${升}^{\frac{磷}{磷-2}}$ 对于边界附近的速度和磁场。