Compressible hydrodynamic flow of liquid crystals in 1-D
Compressible hydrodynamic flow of liquid crystals in 1-D
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DOI：
10.3934/dcds.2012.32.539
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发表时间：
2011-09
影响因子：
1.1
通讯作者：
S. Ding;Junyu Lin;Changyou Wang;Huanyao Wen
中科院分区：
文献类型：
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作者：
S. Ding;Junyu Lin;Changyou Wang;Huanyao Wen
我们考虑一个简化的Ericksen-Leslie方程来模拟一维液晶的可压缩流体动力学流动。若初值$（\rho_0，u_0，n_0）\in C^{1，\alpha}（I）\times C ^{2，\alpha}（I，S^2）\times C ^{2，\alpha}（I，S^2）$且$\rho_0\gec_0>0$，则得到整体经典解的存在唯一性.对于$0\le\rho_0\in H^1（I）$和$（u_0，n_0）\in H^1（I）\times H^2（I，S^2）$，我们得到了整体强解的存在唯一性.
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.