  In this paper, we consider the solutions of the relaxed Q-tensor flow in
$\R^3$ with small parameter $\epsilon$. 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 \cite{struwe88} and \cite{keller}, where Ginzburg-Landau
approximation approach was used.
