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Original Article

On the Isotropic–Nematic Phase Transition for the Liquid Crystal

School of Mathematics and Computer Sciences, Anhui Normal University, Wuhu, 241002, China
Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
School of Mathematical Sciences, Peking University, Beijing, 100871, China
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Abstract

In this paper, we study the isotropic–nematic phase transition for the nematic liquid crystal based on the Landau–de Gennes Q-tensor theory. We justify the limit from the Landau–de Gennes flow to a sharp interface model: in the isotropic region, Q0; in the nematic region, the Q-tensor is constrained on the manifolds N={s+(nn13I),nS2} with s+ a positive constant, and the evolution of alignment vector field n obeys the harmonic map heat flow, while the interface separating the isotropic and nematic regions evolves by the mean curvature flow. This problem can be viewed as a concrete but representative case of the Rubinstein–Sternberg–Keller problem introduced in Rubinstein et al. (SIAM J. Appl. Math. 49:116–133, 1989; SIAM J. Appl. Math. 49:1722–1733, 1989).

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Peking Mathematical Journal
Pages 141-219
Cite this article:
Fei, M., Wang, W., Zhang, P. et al. On the Isotropic–Nematic Phase Transition for the Liquid Crystal. Peking Math J 1, 141-219 (2018). https://doi.org/10.1007/s42543-018-0005-3

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Received: 06 May 2018
Accepted: 21 September 2018
Published: 24 October 2018
© Peking University 2018
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