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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


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.


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

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