Four-thirds law of energy and magnetic helicity in electron and Hall magnetohydrodynamic fluids

In this paper, by exploiting the feature of the Hall term, we establish some local version four-thirds laws for the dissipation rates of energy and magnetic helicity in both the inviscid electron and Hall magnetohydrodynamic equations in the sense of Duchon-Robert type. Four-thirds law involving the dissipation rates of energy for the Hall magnetohydrodynamic equations generalizes corresponding the work of Galtier and new 4/3 laws for the dissipation rates of magnetic helicity in these systems are first observed. To this end, we derive local Karman-Howarth-Monin type equations of the energy and magnetic helicity in these equations.(c) 2023 Elsevier B.V. All rights reserved.