301. Compressible hydrodynamic flow of liquid crystals in 1-D
- Author
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Changyou Wang, Huanyao Wen, Shijin Ding, and Junyu Lin
- Subjects
Physics ,Strong solutions ,Liquid crystal ,Applied Mathematics ,Dimension (graph theory) ,Compressibility ,Discrete Mathematics and Combinatorics ,Uniqueness ,Analysis ,Hydrodynamic flow ,Mathematical physics - 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.
- Published
- 2012
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