In this paper, we provide sufficient conditions for the energy conservation of the DiPerna–Lions solutions given in DiPerna and Lions (Commun Pure Appl Math 42:729–757, 1989), Rein (Commun Math Sci 2:145–158, 2004) to Vlasov–Maxwell systems in R 3 , which requires only macroscopic density ρ ∈ L t 2 L loc 2 for the relativistic case and | ξ | f ∈ L t , x 2 L ξ 1 for the non-relativistic case, improving the results in Sospedra–Alfonso (Commun Math Sci 8:901–908, 2010), Bardos et al. (Q Appl Math 78:193–217, 2020). Next, by mollification in time twice with different parameters and the weak formulations containing t = 0 , we obtain the same results for solutions given in Guo (Commun Math Phys 154:245–263, 1993) with low temporal regularity to the Vlasov–Maxwell systems in bounded domains under some boundary-layer conditions. [ABSTRACT FROM AUTHOR]