Shinbrot’s energy conservation criterion for the 3D Navier–Stokes–Maxwell system - Ma, Dandan; Wu, Fan (Comptes Rendus. Mathématique)
This paper concerns the energy conservation for the weak solutions to the Navier–Stokes–Maxwell system. Although the Maxwell equation with hyperbolic nature, we still establish a $L^qL^p$ type condition guarantee validity of the energy equality for the weak solutions. We mention that there no regularity assumption on the electric field $E$.