This article addresses the global regularity (in time) issue of two dimensional incompressible micropolar equations with various partial dissipations. Micropolar fluids represent a class of fluids with nonsymmetric stress tensor (called polar fluids) such as fluids consisting of suspending particles, dumbbell molecules, etc. Whether or not its classical solutions of 2D micropolar equations without velocity dissipation and micro-rotational viscosity develop finite time singularities is a difficult problem, and remains open. Here, we mainly focus on two types of partial dissipation cases, and we prove the conditional global regularity.
Published November 15, 2017.
Math Subject Classifications: 35Q35, 35B35, 35B65, 76D03.
Key Words: Global regularity; micro-polar equations; partial dissipation.
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| Dipendra Regmi |
Department of Mathematics
University of North Georgia
3820 Mundy Mill Rd
Oakwood, GA 30566, USA
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