Global Solution to the Three-Dimensional Compressible Flow of Liquid Crystals
Global Solution to the Three-Dimensional Compressible Flow of Liquid Crystals
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DOI：
10.1137/120898814
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发表时间：
2012-06
期刊：
影响因子：
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通讯作者：
Xianpeng Hu;Hao-qing Wu
中科院分区：
文献类型：
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作者：
Xianpeng Hu;Hao-qing Wu
研究了向列液晶三维可压缩流动的柯西问题。当初始基准在S^2$中具有常数向量$\hat{{\bf d}}\时，接近于平衡状态$(1,{\bf 0}, \hat{{\bf d}}})$时，证明了该全局强解在临界Besov空间中的存在唯一性。通过对流项适当线性化系统的局部适定性和一致估计，证明了系统的整体存在性。
The Cauchy problem for the three-dimensional compressible flow of nematic liquid crystals is considered. Existence and uniqueness of the global strong solution are established in critical Besov spaces provided that the initial datum is close to an equilibrium state $(1,{\bf 0}, \hat{{\bf d}})$ with a constant vector $\hat{{\bf d}}\in S^2$. The global existence result is proved via the local well-posedness and uniform estimates for proper linearized systems with convective terms.