Global well-posedness and decay of smooth solutions to the non-isothermal model for compressible nematic liquid crystals

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• 作者：Boling Guo^a ; ^{gbl@iacpm.ac.cn} ; Xiaoyu Xi^b ; ^{xixiaoyu1357@126.com} ; Binqiang Xie^b ; ^{xbq211@163.com}
• 关键词：76N10 ; 35Q30 ; 35Q35
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：1413-1460
• 全文大小：535 K
• 卷排序：262

文摘

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 LqLq–LpLp estimates and the Fourier splitting method, if the initial perturbation is small in H3H3-norm and bounded in LqLq (q∈[1,65)) 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 L2L2-norm are achieved.