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Global well-posedness for the cubic fractional Schrödinger equation

Volume 153 / 2018

Xinjun Gao 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.

Authors

  • Xinjun GaoDepartment of Mathematical Sciences
    University of Science and Technology of China
    Hefei 230026, China
    and
    The Graduate School of
    China Academy of Engineering Physics
    P.O. Box 2101
    Beijing 100088, China
    e-mail

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