Regularity Results on the Leray-alpha Magnetohydrodynamics Systems
نویسنده
چکیده
We study certain generalized Leray-alpha magnetohydrodynamics systems. We show that the solution pairs of velocity and magnetic fields to this system in two-dimension preserve their initial regularity in two cases: dissipation logarithmically weaker than a full Laplacian and zero diffusion, zero dissipation and diffusion logarithmically weaker than a full Laplacian. These results extend previous results in [41]. Moreover, we show that for a certain three-dimensional Leray-alpha magnetohydrodynamics system, sufficient condition of regularity may be reduced to a horizontal gradient or a partial derivative in just one direction of the magnetic field, reducing components from the results in [11].
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