Energy conservation for the compressible ideal Hall-MHD equations

Abstract

In this paper, we study the regularity and energy conservation of the weak solutions for compressible ideal Hall-magnetohydrodynamic (Hall-MHD) system, where $ (t, x)\in(0, T)\times {\mathbb{T}}^d(d\geq\; 1) $. By exploring the special structure of the nonlinear terms in the model, we obtain the sufficient conditions for the regularity of the weak solutions for energy conservation. Our main strategy relies on commutator estimates.

Keywords

• compressible ideal hall-mhd system
• regularity
• energy conservation