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Volume 52, Issue 1
Regularity Criteria on the 2D Anisotropic Magnetic Bénard Equations

Dipendra Regmi & Ramjee Sharma

DOI: 10.4208/jms.v52n1.19.06

J. Math. Study, 52 (2019), pp. 60-74.

Published online: 2019-03

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  • 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.

  • Keywords

Global regularity, magnetic Bénard equations, partial dissipation.

  • AMS Subject Headings

35Q35, 35B35, 35B65, 76D03

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

regmid@farmingdale.edu (Dipendra Regmi)

ramjee.sharma@ung.edu (Ramjee Sharma)

  • BibTex
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  • TXT
@Article{JMS-52-60, author = {Regmi , Dipendra and Sharma , Ramjee}, title = {Regularity Criteria on the 2D Anisotropic Magnetic Bénard Equations}, journal = {Journal of Mathematical Study}, year = {2019}, volume = {52}, number = {1}, pages = {60--74}, 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v52n1.19.06}, url = {http://global-sci.org/intro/article_detail/jms/13049.html} }
TY - JOUR T1 - Regularity Criteria on the 2D Anisotropic Magnetic Bénard Equations AU - Regmi , Dipendra AU - Sharma , Ramjee JO - Journal of Mathematical Study VL - 1 SP - 60 EP - 74 PY - 2019 DA - 2019/03 SN - 52 DO - http://doi.org/10.4208/jms.v52n1.19.06 UR - https://global-sci.org/intro/article_detail/jms/13049.html KW - Global regularity, magnetic Bénard equations, partial dissipation. AB -

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.

Dipendra Regmi & Ramjee Sharma. (2019). Regularity Criteria on the 2D Anisotropic Magnetic Bénard Equations. Journal of Mathematical Study. 52 (1). 60-74. doi:10.4208/jms.v52n1.19.06
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