Compressible hydrodynamic flow of liquid crystals in 1-D

Shijin Ding; Junyu Lin; Changyou Wang; Huanyao Wen

doi:10.3934/dcds.2012.32.539

Article Contents

2012, Volume 32, Issue 2: 539-563. Doi: 10.3934/dcds.2012.32.539

This issue Previous Article On some geometry of propagation in diffractive time scales Next Article Genus and braid index associated to sequences of renormalizable Lorenz maps

Compressible hydrodynamic flow of liquid crystals in 1-D

1.
Department of Mathematics, South China Normal University, Guangzhou, Guangdong 510631
2.
Department of Mathematics, South China University of Technology, Guangzhou, 510640
3.
Department of Mathematics, University of Kentucky, Lexington, KY 40513
4.
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631

Received: October 31, 2010

Revised: April 30, 2011

Published: January 2012

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Abstract

We consider a simplified version of Ericksen-Leslie equation modeling the compressible hydrodynamic flow of nematic liquid crystals in dimension one. If the initial data $(\rho_0, u_0,n_0)\in C^{1,\alpha}(I)\times C^{2,\alpha}(I)\times C^{2,\alpha}(I, S^2)$ and $\rho_0\ge c_0>0$, then we obtain both existence and uniqueness of global classical solutions. For $0\le\rho_0\in H^1(I)$ and $(u_0, n_0)\in H^1(I)\times H^2(I,S^2)$, we obtain both existence and uniqueness of global strong solutions.

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Mathematics Subject Classification: Primary: 35K55, 76N10.

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References

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