Global well-posedness and decay of smooth solutions to the non-isothermal model for compressible nematic liquid crystals
Global well-posedness and decay of smooth solutions to the non-isothermal model for compressible nematic liquid crystals
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DOI：
10.1016/j.jde.2016.10.015
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发表时间：
2017-02
影响因子：
2.4
通讯作者：
B. Guo;Xiaoyu Xi;Binqiang Xie
中科院分区：
文献类型：
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作者：
B. Guo;Xiaoyu Xi;Binqiang Xie
本文考虑可压缩液晶三维非等温模型的柯西问题。当初始数据接近于稳态（ρ <$，0，d <$，0 <$）时，建立了时间上全局光滑解的存在性.利用Lq-Lp估计和Fourier分裂方法，当初始扰动在H3范数下很小且在Lq（q∈[1，65））范数下有界时，得到了解的一阶和二阶空间导数的最优衰减率.此外，还得到了指向矢场d在L2模下的三阶和四阶空间导数.
The Cauchy problem for the three-dimensional non-isothermal model for compressible nematic liquid crystals is considered. Existence of global-in-time smooth solutions is established provided that the initial datum is close to a steady state (ρ¯, 0, d¯, θ¯). By using the L q–L p estimates and the Fourier splitting method, if the initial perturbation is small in H 3-norm and bounded in L q (q∈[1, 6 5)) norm, we obtain the optimal decay rates for the first and second order spatial derivatives of solutions. In addition, the third and fourth order spatial derivatives of director field d in L 2-norm are achieved.