On well-posedness for nonlinear Schrödinger equations with power nonlinearity in fractional order Sobolev spaces

We study the well-posedness for the nonlinear Schrödinger equation (NLS) i∂tu+12Δu=λ|u|p−1u in R1+n, where p>1,λ∈C, and prove that (NLS) is locally well-posed in Hs if 2