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From the Q-Tensor Flow for the Liquid Crystal to the Harmonic Map Flow

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Abstract

In this paper, we consider the solutions of the relaxed Q-tensor flow in \({\mathbb{R}^3}\) with small parameter \({\epsilon}\). We show that the limiting map is the so-called harmonic map flow. As a consequence, we present a new proof for the global existence of a weak solution for the harmonic map flow in three dimensions as in [18, 23], where the Ginzburg–Landau approximation approach was used.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Meng Wang

  2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Wendong Wang

  3. School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Zhifei Zhang

Authors
  1. Meng Wang
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  2. Wendong Wang
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  3. Zhifei Zhang
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Correspondence to Wendong Wang.

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Communicated by W. E

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Wang, M., Wang, W. & Zhang, Z. From the Q-Tensor Flow for the Liquid Crystal to the Harmonic Map Flow. Arch Rational Mech Anal 225, 663–683 (2017). https://doi.org/10.1007/s00205-017-1111-6

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  • DOI: https://doi.org/10.1007/s00205-017-1111-6

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