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Logarithmically extended global regularity result of Lans-alpha MHD system in two-dimensional space. (English) Zbl 1311.35186
Summary: We study the two-dimensional generalized Lans alpha magnetohydrodynamics system. We show that the solution pairs of velocity and magnetic fields to this system 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.

MSC:
35Q30 Navier-Stokes equations
76W05 Magnetohydrodynamics and electrohydrodynamics
76D05 Navier-Stokes equations for incompressible viscous fluids
35B65 Smoothness and regularity of solutions to PDEs
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