Energy conservation for the weak solutions to the ideal inhomogeneous magnetohydrodynamic equations in a bounded domain

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.