Hölder regularity of solutions and physical quantities for the ideal electron magnetohydrodynamic equations

In this paper, we make the first attempt to figure out the differences on Hölder regularity in time of solutions and conserved physical quantities between the ideal electron magnetohydrodynamic equations concerning Hall term and the incompressible Euler equations involving convection term. It is shown that the regularity in time of magnetic field B B is C t α 2 Cₜ^{ {α }2} provided it belongs to L t ∞ C x α Lₜ∞ Cₓα for any α > 0 α >0 , its energy is C t 2 α 2 − α Cₜ2α /2-α as long as B B belongs to L t ∞ B ˙ 3 , ∞ α Lₜ∞ Ḃα3,∞ for any 0 > α > 1 0>α >1 and its magnetic helicity is C t 2 α + 1 2 − α Cₜ2α +1/2-α supposing B B belongs to L t ∞ B ˙ 3 , ∞ α Lₜ∞ Ḃα3,∞ for any 0 > α > 1 2 0>α > 12 , which are quite different from the classical incompressible Euler equations.