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Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions

  • * Corresponding author: Yangjun Ma

    * Corresponding author: Yangjun Ma

This work is supported by the grants from the National Natural Foundation of China under contract No. 11971360

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  • 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 $ \epsilon $ for both the compressible system and its differential system with respect to time under uniformly in $ \epsilon $ small initial data. Then, based on these uniform estimates, we pass to the limit in the compressible system as $ \epsilon \rightarrow 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.

    Mathematics Subject Classification: Primary: 35D35, 76W05, 76E19, 35B40; Secondary: 76A15.


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