The Global Cauchy Problem for the Critical and Subcritical Nonlinear Schrodinger Equations in Hs (Journal of Partial Differential Equations, 1998)
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.
Keywords: Nonlinear Schrödinger equation; Cauchy problem; critical and subcritical powers in H^s; global existence