Energy conservation for the nonhomogeneous incompressible Hall-MHD equations in a bounded domain

Abstract

In this paper, we study the energy conservation of the nonhomogeneous incompressible Hall-magnetohydrodynamic equations in a bounded domain Ω⊂Rdwith d=2,3. By exploring the special structure of the nonlinear terms in the Hall-magnetohydrodynamic equations, we obtain the sufficient conditions for the regularity of the weak solutions for energy conservation. The treatment of the boundary terms mainly relies on the coarea formula.

Keywords

• Hall-MHD system
• Regularity
• Energy conservation