Unconditional energy conservation and conditional regularity for the incompressible Navier-Stokes Maxwell system

Abstract

In this paper, we study a hydrodynamic system modeling the evolution of a plasma subject to a self-induced electromagnetic Lorentz force in incompressible viscous fluids. The system consists of the Navier–Stokes equations coupled with a Maxwell equation. In the three dimensional case, we show that every weak solution verifies the energy equality for the incompressible Navier–Stokes–Maxwell equations with damping. We also establish some non-explosion criteria in terms of the velocity and magnetic of local strong solution for standard Navier–Stokes–Maxwell system.

Keywords

• navier–stokes–maxwell system
• damping term
• energy conservation
• non-explosion criteria