On the initial- and boundary-value problem for 2D micropolar equations with only angular velocity dissipation

  • Quansen Jiu
  • Jitao Liu
  • Jiahong Wu
  • Huan Yu


This paper focuses on the initial- and boundary-value problem for the two-dimensional micropolar equations with only angular velocity dissipation in a smooth bounded domain. The aim here is to establish the global existence and uniqueness of solutions by imposing natural boundary conditions and minimal regularity assumptions on the initial data. Besides, the global solution is shown to possess higher regularity when the initial datum is more regular. To obtain these results, we overcome two main difficulties: one due to the lack of full dissipation and one due to the boundary conditions. In addition to the global regularity problem, we also examine the large time behavior of solutions and obtain explicit decay rates.


Bounded domain Global regularity Micropolar equations Partial dissipation 

Mathematics Subject Classification

35Q35 76D03 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesCapital Normal UniversityBeijingPeople’s Republic of China
  2. 2.College of Applied SciencesBeijing University of TechnologyBeijingPeople’s Republic of China
  3. 3.Department of MathematicsOklahoma State UniversityStillwaterUSA
  4. 4.Institute of Applied Physics and Computational MathematicsBeijingPeople’s Republic of China

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