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Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation

Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation
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Year:    2016

Author:    Dipendra Regmi, Jiahong Wu

Journal of Mathematical Study, Vol. 49 (2016), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v49n2.16.05

Journal of Mathematical Study, Vol. 49 (2016), Iss. 2 : pp. 169–194

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Global regularity magneto-micropolar equations partial dissipation.

Author Details

Dipendra Regmi

Jiahong Wu

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