Energy equality for weak solutions to the 3D magnetohydrodynamic equations in a bounded domain

In this paper, we study the energy equality for weak solutions to the 3D homogeneous incompressible magnetohydrodynamic equations with viscosity and magnetic diffusion in a bounded domain. Two types of regularity conditions are imposed on weak solutions to ensure the energy equality. For the first type, some global integrability condition for the velocity \begin{document}$ \mathbf u $\end{document} is required, while for the magnetic field \begin{document}$ \mathbf b $\end{document} and the magnetic pressure \begin{document}$ \pi $\end{document} , some suitable integrability conditions near the boundary are sufficient. In contrast with the first type, the second type claims that if some additional interior integrability is imposed on \begin{document}$ \mathbf b $\end{document} , then the regularity on \begin{document}$ \mathbf u $\end{document} can be relaxed.