Hs solutions for nonlinear Schrödinger equations with potentials superquadratic at infinity

In this Letter we study the initial value problem for the nonlinear Schrödinger equation with the potential V superquadratic at infinity. With the local smoothing property and Strichartz inequality obtained by the authors, we prove the existence and the uniqueness of the solution for Hs-valued initial data and fractional s by combining the L2 boundedness theory of pseudo differential operators and the fractional derivatives estimate.