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Finite Time Singularity of the Nematic Liquid Crystal Flow in Dimension Three

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Abstract

In this paper, we consider the initial and boundary value problem of a simplified nematic liquid crystal flow in dimension three and construct two examples of finite time singularity. The first example is constructed within the class of axisymmetric solutions, while the second example is constructed for any generic initial data \({(u_0,d_0)}\) that has sufficiently small energy, and \({d_0}\) has a nontrivial topology.

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Author notes

  1. Tao Huang

    Present address: NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China

Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Tao Huang & Chun Liu

  2. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    Fanghua Lin

  3. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907, USA

    Changyou Wang

Authors
  1. Tao Huang
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  2. Fanghua Lin
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  3. Chun Liu
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  4. Changyou Wang
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Correspondence to Changyou Wang.

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Communicated by V. Šverák

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Huang, T., Lin, F., Liu, C. et al. Finite Time Singularity of the Nematic Liquid Crystal Flow in Dimension Three. Arch Rational Mech Anal 221, 1223–1254 (2016). https://doi.org/10.1007/s00205-016-0983-1

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  • DOI: https://doi.org/10.1007/s00205-016-0983-1

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