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

Yang Liu; Sining Zheng; Huapeng Li; Shengquan Liu

doi:10.3934/dcds.2017165

Article Contents

2017, Volume 37, Issue 7: 3921-3938. Doi: 10.3934/dcds.2017165

This issue Previous Article Existence of SRB measures for a class of partially hyperbolic attractors in banach spaces Next Article Dynamical properties of nonautonomous functional differential equations with state-dependent delay

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
* Corresponding author: S. Zheng

Received: June 30, 2015

Revised: January 31, 2017

Published: August 2017

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Abstract

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.

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Mathematics Subject Classification: 76W05, 76N10, 35B45.

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