Regularity Criteria on the 2D Anisotropic Magnetic Bénard Equations (Journal of Mathematical Study, 2019)
In this paper, we study the global regularity issue of two dimensional incompressible magnetic Bénard equations with partial dissipation and magnetic diffusion. It remains open whether the smooth initial data produce solutions that areglobally regular in time for all values of the parameters involved in the equations. Wepresent conditional global regularity of the solutions. Moreover, we prove the globalregularity for the slightly regularized system.
Keywords: Global regularity; magnetic Bénard equations; partial dissipation.