# American Institute of Mathematical Sciences

March  2011, 15(2): 357-371. doi: 10.3934/dcdsb.2011.15.357

## Weak solution to compressible hydrodynamic flow of liquid crystals in dimension one

 1 Department of Mathematics, South China Normal University, Guangzhou, Guangdong 510631 2 Department of Mathematics, University of Kentucky, Lexington, KY 40513, United States 3 School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

Received  November 2009 Revised  March 2010 Published  December 2010

We consider the equation modeling the compressible hydrodynamic flow of liquid crystals in one dimension. In this paper, we establish the existence of a weak solution $(\rho, u,n)$ of such a system when the initial density function $0\le \rho_0 \in L^\gamma$ for $\gamma>1$, $u_0\in L^2$, and $n_0\in H^1$. This extends a previous result by [12], where the existence of a weak solution was obtained under the stronger assumption that the initial density function $0$<$c\le \rho_0\in H^1$, $u_0\in L^2$, and $n_0\in H^1$.
Citation: Shijin Ding, Changyou Wang, Huanyao Wen. Weak solution to compressible hydrodynamic flow of liquid crystals in dimension one. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 357-371. doi: 10.3934/dcdsb.2011.15.357
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##### References:
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