In this interesting paper, the authors establish the local well-posedness and blow-up criteria of strong solutions to the Ericksen-Leslie system in \(\mathbb{R}^3\) for the Oseen-Frank model. This model is used in the static theory of nematic liquid crystals. There is a unit vector field \(u\) in a region \(\Omega \subset\mathbb{R}^3\) as well the Oseen-Frank density \(W (u, \nabla u)\) is \[ W (u, \nabla u) = k_1 (\mathrm{div} u)^2 + k_2 (u \cdot \mathrm{curl} u)^2 + k_3 |u \times \mathrm{curl} u|^2 + k_4 [\mathrm{tr}(\nabla u)^2 - (\mathrm{div} u)^2 ], \] where \(k_1\), \(k_2\), \(k_3\), \(k_4\) are positive constants. The free energy for the state \(u\in H^1(\Omega ;S^2)\) is defined by \(E(u;\Omega )=\int_{\Omega }W(u,\nabla u)dx\), then the Euler-Lagrange system for the Oseen-Frank energy \(E(u,\Omega )\) is determined. The dynamic motion of the liquid crystals is described by the Ericksen-Leslie system. Note that the divergence of \(\mathrm{tr}(\nabla u)^2 - (\mathrm{div} u)^2\) is free, therefore, \[ W (u, \nabla u) = a|\nabla u|^2 + V (u, \nabla u), \] where \(a = \min\{k_1, k_2, k_3 \} > 0\), and \[ V (u, \nabla u) = (k_1 - a)(\mathrm{div} u)^2 + (k_2 - a)(u \cdot \mathrm{curl} u)^2 + (k_3 - a)|u \times \mathrm{curl} u|^2. \] Having in mind the above stated notation, one may write the Ericksen-Leslie system containing a finite number of PDEs, that is, the Navier-Stokes system coupled with the gradient flow for the Oseen-Frank model, considered as an extension of the harmonic map flow. Here, the authors consider the Cauchy problem with some initial data to the Ericksen-Leslie system for the general Oseen-Frank model in \(\mathbb{R}^3\), as the velocity vector \(v_0\) (\(\mathrm{div} v_0=0\)) and the initial state \(u_0\) (\(|u_0|=1\)) are in the classes \(H^1(\mathbb{R}^3)\) and \(H^2(\mathbb{R}^3)\). The main result is that the above mentioned Cauchy problem has a unique solution \((u,v)\) in \(\mathbb{R}^3\times (0,T^{\ast })\) for some positive number \(T^{\ast }\) (the blowing up point) depending only on the initial data. The blow up criteria to strong solutions to the Ericksen-Leslie system are given. It is shown that strong solutions of the Ginzburg-Landau approximate system converge to strong solution of the Ericksen-Leslie system up to the maximal existence time. The blow-up effect is discussed as well.