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Global Existence and Large Time Behavior of Strong Solutions to the 2-D Compressible Nematic Liquid Crystal Flows with Vacuum

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Abstract

This paper is concerned with the strong solutions to the Cauchy problem of a simplified Ericksen-Leslie system of compressible nematic liquid crystals in two or three dimensions with vacuum as far field density. For strong solutions, some a priori decay rate (in large time) for the pressure, the spatial gradient of velocity field and the second spatial gradient of liquid crystal director field are obtained provided that the initial total energy is suitably small. Furthermore, with the help of the key decay rates, we establish the global existence and uniqueness of strong solutions (which may be of possibly large oscillations) in two spatial dimensions.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Beijing Forestry University, Beijing, 100083, People’s Republic of China

    Teng Wang

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  1. Teng Wang
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Correspondence to Teng Wang.

Additional information

Communicated by G.-Q. Chen

The research was supported by the Fundamental Research Funds for the Central Universities No. BLX2015-27.

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Wang, T. Global Existence and Large Time Behavior of Strong Solutions to the 2-D Compressible Nematic Liquid Crystal Flows with Vacuum. J. Math. Fluid Mech. 18, 539–569 (2016). https://doi.org/10.1007/s00021-016-0251-z

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