Well-posedness and Scattering for the Critical Fractional Schrödinger Equations

Abstract

We consider the Cauchy problem for the critical fractional Schrödinger equation with the power type nonlinearity. Hong-Sire [13] proved the local well-posedness, small data global wellposedness and scattering in cases of P > 5 when d = 1 and P > 3 when d ≥ 2. In this paper, we extend the results to the cases of P = 5 when d = 1 and P = 3 when d ≥ 2 by using U^p, V^p spaces introduced by Koch-Tataru [16, 17].