Regularity Criteria on the 2D Anisotropic Magnetic Bénard Equations

Authors

  • Dipendra Regmi Department of Mathematics, Farmingdale State College, SUNY, 2350 Broadhollow Road, Farmingdale, NY 11735
  • Ramjee Sharma Department of Mathematics, University of North Georgia, 3820 Mundy Mill Rd, Oakwood, GA 30566, USA

DOI:

https://doi.org/10.4208/jms.v52n1.19.06

Keywords:

Global regularity, magnetic Bénard equations, partial dissipation.

Abstract

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 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.

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Published

2019-03-06

Issue

Vol. 52 No. 1 (2019)

Section

Articles