Global existence and convergence rates for the 3-D compressible micropolar equations without heat conductivity

ABSTRACT

In this paper, the 3-D full compressible micropolar fluid with positive constant viscosity but with zero heat conductivity is considered. Global well-posedness and optimal convergence rates are established for any small $H^3$ initial data and bounded $L^1$-norm by combining the local existence and a priori estimates. A priori decay-in-time estimates on the pressure and velocity are used to get the uniform bound of entropy.

Keywords:

• Global existence
• convergence rates
• micropolar fluid

2010 Mathematics Subject Classifications:

• 35B65
• 35Q20
• 35H10

Acknowledgments

The authors express much gratitude to Professor Huijiang Zhao for his supports.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the ‘Fundamental Research Funds for the Central Universities’ and by the grant from National Natural Science Foundation of China (contract numbers 11671309).