  For the Landau-de Gennes functional on 3D domains, \begin{equation*}
I_{\varepsilon}(Q,\Omega):=\int_{\Omega}\left\{\frac{1}{2}|\nabla
Q|^2+\frac{1}{\varepsilon^2}\left(
-\frac{a^2}{2}\mathrm{tr}(Q^2)-\frac{b^2}{3}\mathrm{tr}(Q^3)+\frac{c^2}{4}[\mathrm{tr}(Q^2)]^2
\right) \right\}\,dx, \end{equation*} it is well-known that under suitable
boundary conditions, the global minimizer $Q_\varepsilon$ converges strongly in
$H^1(\Omega)$ to a uniaxial minimizer $Q_*=s_+(n_*\otimes
n_*-\frac{1}{3}\mathrm{Id})$ up to some subsequence
$\varepsilon_n\rightarrow\infty$ , where $n_*\in H^1(\Omega,\mathbb{S}^2)$ is a
minimizing harmonic map. In this paper we further investigate the structure of
$Q_{\varepsilon}$ near the core of a point defect $x_0$ which is a singular
point of the map $n_*$. The main strategy is to study the blow-up profile of
$Q_{\varepsilon_n}(x_n+\varepsilon_n y)$ where $\{x_n\}$ are carefully chosen
and converge to $x_0$. We prove that $Q_{\varepsilon_n}(x_n+\varepsilon_n y)$
converges in $C^2_{loc}(\mathbb{R}^n)$ to a tangent map $Q(x)$ which at
infinity behaves like a "hedgehog" solution that coincides with the asymptotic
profile of $n_*$ near $x_0$. Moreover, such convergence result implies that the
minimizer $Q_{\varepsilon_n}$ can be well approximated by the Oseen-Frank
minimizer $n_*$ outside the $O(\varepsilon_n)$ neighborhood of the point
defect.
