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Global existence for slightly compressible hydrodynamic flow of liquid crystals in two dimensions

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Abstract

In two dimensions, we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions. As shown by Ding et al. (2013), when the parameter λ → ∞, the solutions to the compressible liquid crystal system approximate that of the incompressible one. Furthermore, Ding et al. (2013) proved that the regular incompressible limit solution is global in time with small enough initial data. In this paper, we show that the solution to the compressible liquid crystal flow also exists for all time, provided that λ is sufficiently large and the initial data are almost incompressible.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    ShiJin Ding & JinRui Huang

  2. Department of Mathematics, South China University of Technology, Guangzhou, 510640, China

    JunYu Lin

Authors
  1. ShiJin Ding
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  2. JinRui Huang
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  3. JunYu Lin
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Correspondence to JinRui Huang.

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Ding, S., Huang, J. & Lin, J. Global existence for slightly compressible hydrodynamic flow of liquid crystals in two dimensions. Sci. China Math. 56, 2233–2250 (2013). https://doi.org/10.1007/s11425-013-4620-2

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  • DOI: https://doi.org/10.1007/s11425-013-4620-2

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