  In this paper, we show the existence and uniqueness of local regular
solutions to the initial-Neumann boundary value problem of Schr\"{o}dinger flow
from a smooth bounded domain $\Omega\subset\mathbb{R}^3$ into
$\mathbb{S}^2$(namely Landau-Lifshitz equation without dissipation). The proof
is built on a parabolic perturbation method, an intrinsic geometric energy
argument and some observations on the behaviors of some geometric quantities on
the boundary of the domain manifold. It is based on methods from Ding and Wang
(one of the authors of this paper) for the Schr\"odinger flows of maps from a
closed Riemannian manifold into a K\"ahler manifold as well as on methods by
Carbou and Jizzini for solutions of the Landau-Lifshitz equation.
