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In this paper, by exploiting the feature of the Hall term, we establish somelocal version four-thirds laws for the dissipation rates of energy and magnetichelicity in both electron and Hall magnetohydrodynamic equations in the senseof Duchon-Robert type. New 4/3 laws for the dissipation rates of magnetichelicity in these systems are first observed and four-thirds law involving thedissipation rates of energy for the Hall magnetohydrodynamic equationsgeneralizes the work of Galtier.

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