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On the Isotropic–Nematic Phase Transition for the Liquid Crystal
Peking Mathematical Journal 2018, 1 (2): 141-219
Published: 24 October 2018
Abstract Collect

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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