Volume 49, Issue 2
Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation

Dipendra Regmi & Jiahong Wu

J. Math. Study, 49 (2016), pp. 169-194.

Published online: 2016-07

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  • Abstract
This paper studies the global existence and regularity of classical solutions to the 2D incompressible magneto-micropolar equations with partial dissipation. The magneto-micropolar equations model the motion of electrically conducting micropolar fluids in the presence of a magnetic field. When there is only partial dissipation, the global regularity problem can be quite difficult. We are able to single out three special partial dissipation cases and establish the global regularity for each case. As special consequences, the 2D Navier-Stokes equations, the 2D magnetohydrodynamic equations, and the 2D micropolar equations with several types of partial dissipation always possess global classical solutions. The proofs of our main results rely on anisotropic Sobolev type inequalities and suitable combination and cancellation of terms.
  • Keywords

Global regularity magneto-micropolar equations partial dissipation

  • AMS Subject Headings

35Q35, 35B35, 35B65, 76D03

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

regmid@farmingdale.edu (Dipendra Regmi)

jiahong.wu@okstate.edu (Jiahong Wu)

  • BibTex
  • RIS
  • TXT
@Article{JMS-49-169, author = {Regmi , Dipendra and Wu , Jiahong}, title = {Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation}, journal = {Journal of Mathematical Study}, year = {2016}, volume = {49}, number = {2}, pages = {169--194}, abstract = {This paper studies the global existence and regularity of classical solutions to the 2D incompressible magneto-micropolar equations with partial dissipation. The magneto-micropolar equations model the motion of electrically conducting micropolar fluids in the presence of a magnetic field. When there is only partial dissipation, the global regularity problem can be quite difficult. We are able to single out three special partial dissipation cases and establish the global regularity for each case. As special consequences, the 2D Navier-Stokes equations, the 2D magnetohydrodynamic equations, and the 2D micropolar equations with several types of partial dissipation always possess global classical solutions. The proofs of our main results rely on anisotropic Sobolev type inequalities and suitable combination and cancellation of terms.}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n2.16.05}, url = {http://global-sci.org/intro/article_detail/jms/997.html} }
TY - JOUR T1 - Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation AU - Regmi , Dipendra AU - Wu , Jiahong JO - Journal of Mathematical Study VL - 2 SP - 169 EP - 194 PY - 2016 DA - 2016/07 SN - 49 DO - http://doi.org/10.4208/jms.v49n2.16.05 UR - https://global-sci.org/intro/article_detail/jms/997.html KW - Global regularity KW - magneto-micropolar equations KW - partial dissipation AB - This paper studies the global existence and regularity of classical solutions to the 2D incompressible magneto-micropolar equations with partial dissipation. The magneto-micropolar equations model the motion of electrically conducting micropolar fluids in the presence of a magnetic field. When there is only partial dissipation, the global regularity problem can be quite difficult. We are able to single out three special partial dissipation cases and establish the global regularity for each case. As special consequences, the 2D Navier-Stokes equations, the 2D magnetohydrodynamic equations, and the 2D micropolar equations with several types of partial dissipation always possess global classical solutions. The proofs of our main results rely on anisotropic Sobolev type inequalities and suitable combination and cancellation of terms.
Dipendra Regmi & Jiahong Wu. (2019). Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation. Journal of Mathematical Study. 49 (2). 169-194. doi:10.4208/jms.v49n2.16.05
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