  We proved the local well-posedness for the power-type nonlinear
semi-relativistic or half-wave equation (NLHW) in Sobolev spaces. Our proofs
mainly bases on the contraction mapping argument using Strichartz estimate. We
also apply the technique of Christ-Colliander- Tao in
\cite{ChristCollianderTao} to prove the ill-posedness for (NLHW) in some cases
of the super-critical range.
