# American Institute of Mathematical Sciences

December  2016, 9(6): 1913-1937. doi: 10.3934/dcdss.2016078

## Well-posedness for the three-dimensional compressible liquid crystal flows

 1 College of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China 2 Institute of Applied Physics & Computational Math., Beijing 100088

Received  July 2015 Revised  September 2016 Published  November 2016

This paper is concerned with the initial-boundary value problem for the three-dimensional compressible liquid crystal flows. The system consists of the Navier-Stokes equations describing the evolution of a compressible viscous fluid coupled with various kinematic transport equations for the heat flow of harmonic maps into $\mathbb{S}^2$. Assuming the initial density has vacuum and the initial data satisfies a natural compatibility condition, the existence and uniqueness is established for the local strong solution with large initial data and also for the global strong solution with initial data being close to an equilibrium state. The existence result is proved via the local well-posedness and uniform estimates for a proper linearized system with convective terms.
Citation: Xiaoli Li, Boling Guo. Well-posedness for the three-dimensional compressible liquid crystal flows. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1913-1937. doi: 10.3934/dcdss.2016078
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