Communications in Mathematical Sciences

Volume 18 (2020)

Number 5

Global classical solutions to 1D full compressible micropolar fluids with the Neumann/Robin boundary conditions and vacuum

Pages: 1337 – 1382



Peixin Zhang (School of Mathematical Sciences, Huaqiao University, Quanzhou, China)

Changjiang Zhu (School of Mathematics, South China University of Technology, Guangzhou, China)


In this paper, we consider the initial boundary value problem for the one-dimensional micropolar fluids for viscous compressible and heat-conducting fluids in a bounded domain with the Neumann/Robin boundary conditions on temperature. There are few results until now about global existence of regular solutions to the equations of hydrodynamics with the Robin boundary conditions on temperature. By the analysis of the effect of boundary dissipation, we derive the global existence of classical solution to the corresponding initial boundary value problem with large initial data and vacuum.


compressible micropolar fluids, heat-conducting fluids, vacuum, global classical solutions

2010 Mathematics Subject Classification

35K65, 35Q30, 76N10

The authors’ research was supported by the National Natural Science Foundation of China #11701192, 11771150, 11831003, 11926346 and Guangdong Basic and Applied Basic Research Foundation #2020B1515310015.

Received 28 October 2019

Accepted 28 February 2020

Published 23 September 2020