The Global Cauchy Problem for the Critical and Subcritical Nonlinear Schrodinger Equations in Hs

Abstract

In this paper, the local and global existence of solutions for the Cauchy problem of the critical and subcritical nonlinear Schrödinger equations in H^s (s ≥ 2) is studied by using the manner of formal differentiation with respect to time. Some conjectures posed by Cazenave and Weissler in [1] are verified.