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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