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

Shijin Ding; Changyou Wang; Huanyao Wen

doi:10.3934/dcdsb.2011.15.357

Article Contents

2011, Volume 15, Issue 2: 357-371. Doi: 10.3934/dcdsb.2011.15.357

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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
3.
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631

Received: October 31, 2009

Revised: February 28, 2010

Published: August 2011

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Abstract

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 $n_0\in H^1$.

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Mathematics Subject Classification: Primary: 35K55, 35D30.

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References

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