Regularity Criteria on the 2D Anisotropic Magnetic B(e)nard Equations

摘要

In this paper,we study the global regularity issue of two dimensional in-compressible magnetic B(e)nard equations with partial dissipation and magnetic dif-fusion.It remains open whether the smooth initial data produce solutions that are globally regular in time for all values of the parameters involved in the equations.We present conditional global regularity of the solutions.Moreover,we prove the global regularity for the slightly regularized system.