Communications in Mathematical Sciences

Volume 16 (2018)

Number 8

Initial-boundary value problem for 2D micropolar equations without angular viscosity

Pages: 2147 – 2165

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n8.a5

Authors

Jitao Liu (College of Applied Sciences, Beijing University of Technology, Beijing, China)

Shu Wang (College of Applied Sciences, Beijing University of Technology, Beijing, China)

Abstract

This paper concerns the initial-boundary value problem for 2D micropolar equations without angular viscosity in a smooth bounded domain. It is shown that such a system admits a unique and global strong solution. The main contribution of this paper is to fully exploit the structure of this system and establish high order estimates via introducing an auxiliary field which is at the energy level of one order lower than micro-rotation.

Keywords

initial-boundary value problem, 2D micropolar equations, angular viscosity

2010 Mathematics Subject Classification

35Q35, 76D03

Full Text (PDF format)

The authors would like to thank the anonymous referees for their valuable suggestions in improving the original manuscript. J. Liu is supported by National Natural Science Foundation of China (No. 11801018), Beijing Natural Science Foundation (No. 1192001), Youth Backbone Individual Program of the organization department of Beijing (No. 2017000020124G052) and the Basic Research Fund of Beijing University of Technology (No. 006000546318506). S. Wang is supported by National Natural Science Foundation of China (No. 11531010, No. 11771031, No. 11831003), and Qinghai Provincial Natural Science Foundation of China (No. 2017-ZJ-908).

Received 2 February 2018

Accepted 13 August 2018

Published 18 April 2019