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Although the equations of magnetic field $b$ are of hyperbolic type, and the boundary effects are considered, we still prove the global energy equality provided that $ u \\in L^{q}_{loc}\\left(0, T ; L^{p}(\\Omega)\\right)\n  \\text { for any } \\frac{1}{q}+\\frac{1}{p} \\leq \\frac{1}{2}, \\text { with } p \\geq 4,\\text{ and } b \\in L^{r}_{loc}\\left(0, T ; L^{s}(\\Omega)\\right) \\text { for any } \\frac{1}{r}+\\frac{1}{s} \\leq \\frac{1}{2}, \\text { with } s \\geq 4 $. 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Although the equations of magnetic field $b$ are of hyperbolic type, and the boundary effects are considered, we still prove the global energy equality provided that $ u \\in L^{q}_{loc}\\left(0, T ; L^{p}(\\Omega)\\right)\n  \\text { for any } \\frac{1}{q}+\\frac{1}{p} \\leq \\frac{1}{2}, \\text { with } p \\geq 4,\\text{ and } b \\in L^{r}_{loc}\\left(0, T ; L^{s}(\\Omega)\\right) \\text { for any } \\frac{1}{r}+\\frac{1}{s} \\leq \\frac{1}{2}, \\text { with } s \\geq 4 $. 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