The Cauchy problem of Hartree and pure power type nonlinear Schrödinger equations (Harmonic Analysis and Nonlinear Partial Differential Equations)

"Harmonic Analysis and Nonlinear Partial Differential Equations". July 6～8, 2015. edited by Hideo Kubo and Mitsuru Sugimoto. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.This paper is concerned with the Cauchy problem of Hartree (HNLS) and pure power nonlinear Schr odinger equations (PNLS) with L2-subcritical regularity. It is known that the global well-posedness in the scale invariant homogeneous Sobolev space with radial symmetry or some angular regularity was established provided that the initial data have small norm. We generalize these results by new weighted Strichartz estimates