Global well-posedness for the cubic fractional Schrödinger equation
Volume 153 / 2018
Colloquium Mathematicum 153 (2018), 81-96
MSC: Primary 35Q55; Secondary 35Q40.
DOI: 10.4064/cm7257-5-2017
Published online: 12 April 2018
Abstract
We prove the global well-posedness of the Cauchy problem for the $1$-d fractional Schrödinger equation with cubic nonlinearity in Sobolev spaces $H^s(\mathbb {R})$ for $s \gt {1/2}$. The main approach is the “I-method” together with the multilinear multiplier analysis.
