On the focusing energy-critical fractional nonlinear schrödnger equations

Yonggeun Cho, Gyeongha Hwang*, Tohru Ozawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We consider the fractional nonlinear Schrödinger equation (FNLS) with non-local dispersion |∇|α and focusing energy-critical Hartree type nonlinearity [-(|x|-2α * |u|2)u]. We first establish a global well-posedness of radial case in energy space by adopting Kenig-Merle arguments [20] when the initial energy and initial kinetic energy are less than those of ground state, respectively. We revisit and highlight long time perturbation, profile decomposition and localized virial inequality. As an application of the localized virial inequality, we provide a proof for finite time blowup for energy critical Hartree equations via commutator technique introduced in [2].

Original languageEnglish
Pages (from-to)161-192
Number of pages32
JournalAdvances in Differential Equations
Volume23
Issue number3-4
Publication statusPublished - 2018 Mar 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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