Electron. J. Diff. Equ., Vol. 2016 (2016), No. 154, pp. 1-10.

Global well-posedness of the 2D micropolar fluid flows with mixed dissipation

Yan Jia, Wenjuan Wang, Bo-Qing Dong

Abstract:
This article concerns the global well-posedness of the 2D micropolar fluid flows with mixed dissipation:
$$ -\partial_{yy}(-\Delta)^\alpha u_1,\quad -\partial_{xx}(-\Delta)^\alpha u_2,\quad (-\Delta)^\beta w. $$
We prove the existence and uniqueness of global smooth solution of 2D micropolar fluid flows when $\alpha+\beta \geq1/2$.

Submitted May 3, 2016. Published June 21, 2016.
Math Subject Classifications: 35Q35, 76D05.
Key Words: Micropolar fluid flows; mixed dissipation; global regularity.

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Yan Jia
School of Mathematical Sciences
Anhui University, Hefei 230039, China
email: Yanjia@ahu.edu.cn
Wenjuan Wang
School of Mathematical Sciences
Anhui University, Hefei 230039, China
email: wangwenjuan@ahu.edu.cn
Bo-Qing Dong
School of Mathematical Sciences
Anhui University, Hefei 230039, China
email: bqdong@ahu.edu.cn

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