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首页> 外文期刊>Discrete and continuous dynamical systems >LOW MACH NUMBER LIMIT FOR THE COMPRESSIBLE INERTIAL QIAN-SHENG MODEL OF LIQUID CRYSTALS: CONVERGENCE FOR CLASSICAL SOLUTIONS
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LOW MACH NUMBER LIMIT FOR THE COMPRESSIBLE INERTIAL QIAN-SHENG MODEL OF LIQUID CRYSTALS: CONVERGENCE FOR CLASSICAL SOLUTIONS

机译：液晶可压缩惯性Qian-Sheng模型的低马赫数限制：经典解决方案的收敛性

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摘要

In this paper we study the incompressible limit of the compressible inertial Qian-Sheng model for liquid crystal flow. We first derive the uniform energy estimates on the Mach number ∈ for both the compressible system and its differential system with respect to time under uniformly in ∈ small initial data. Then, based on these uniform estimates, we pass to the limit in the compressible system as ∈→ 0, so that we establish the global classical solution of the incompressible system by compactness arguments. We emphasize that, on global in time existence of the incompressible inertial Qian-Sheng model under small size of initial data, the range of our assumptions on the coefficients are significantly enlarged, comparing to the results of De Anna and Zarnescu's work [6]. Moreover, we also obtain the convergence rates associated with L~2-norm with well-prepared initial data.
机译：本文研究了液晶流动可压缩惯性Qian-Sheng模型的不可压缩极限。 我们首先在Mach编号∈上为可压缩系统及其差动系统相对于均匀的初始数据而导出Mach编号的均匀能量估计。 然后，基于这些统一估计，我们将可压缩系统的极限传递为∈→0，以便通过紧凑性参数建立不可压缩系统的全局经典解决方案。 我们强调，在初步数据小规模下的不可压缩惯性Qian-Sheng模型的全球时间上存在，我们对系数的假设范围显着扩大，比较De Anna和Zarnescu的工作[6]。 此外，我们还获得了与L〜2-NOM相关的收敛速率，具有良好准备的初始数据。

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