From the Q-tensor flow for the liquid crystal to the Harmonic map flow

2015/06/04 by Meng Wang, Wang, Meng, Wendong Wang +3 · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1506.01462

openalex publication_date 2015/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the solutions of the relaxed Q-tensor flow in \R³ with small parameter ε. Firstly, we show that the limiting map is the so called harmonic map flow; Secondly, we also present a new proof for the global existence of weak solution for the harmonic map flow in three dimensions as in \citestruwe88 and \citekeller, where Ginzburg-Landau approximation approach was used.

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