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July  2017, 37(7): 3921-3938. doi: 10.3934/dcds.2017165

## Strong solutions to Cauchy problem of 2D compressible nematic liquid crystal flows

 1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China 2 College of Science, Northeast Electric Power University, Jilin 132013, China 3 School of Mathematics, Liaoning University, Shenyang 110036, China

* Corresponding author: S. Zheng

Received  July 2015 Revised  February 2017 Published  April 2017

This paper studies the local existence of strong solutions to the Cauchy problem of the 2D simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows, coupled via $ρ$ (the density of the fluid), $u$ (the velocity of the field), and $d$ (the macroscopic/continuum molecular orientations). Notice that the technique used for the corresponding 3D local well-posedness of strong solutions fails treating the 2D case, because the $L^p$-norm ($p>2$) of the velocity $u$ cannot be controlled in terms only of $ρ^{\frac{1}{2}}u$ and $\nabla u$ here. In the present paper, under the framework of weighted approximation estimates introduced in [J. Li, Z. Liang, On classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations with vacuum, J. Math. Pures Appl. (2014) 640-671] for Navier-Stokes equations, we obtain the local existence of strong solutions to the 2D compressible nematic liquid crystal flows.

Citation: Yang Liu, Sining Zheng, Huapeng Li, Shengquan Liu. Strong solutions to Cauchy problem of 2D compressible nematic liquid crystal flows. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3921-3938. doi: 10.3934/dcds.2017165
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