TY - JOUR
T1 - The Global Cauchy Problem for the Critical and Subcritical Nonlinear Schrodinger Equations in <em>H<sup>s</sup></em>
JO - Journal of Partial Differential Equations
VL - 2
SP - 173
EP - 192
PY - 1998
DA - 1998/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5564.html
KW - Nonlinear Schrödinger equation
KW - Cauchy problem
KW - critical and subcritical powers in H^s
KW - global existence
AB -  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.