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March/April 2018 On the focusing energy-critical fractional nonlinear Schrödinger equations
Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa
Adv. Differential Equations 23(3/4): 161-192 (March/April 2018).

Abstract

We consider the fractional nonlinear Schrödinger equation (FNLS) with non-local dispersion $|\nabla|^{\alpha}$ and focusing energy-critical Hartree type nonlinearity $[-(|x|^{-2{\alpha}}*|u|^2)u]$. 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].

Citation

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Yonggeun Cho. Gyeongha Hwang. Tohru Ozawa. "On the focusing energy-critical fractional nonlinear Schrödinger equations." Adv. Differential Equations 23 (3/4) 161 - 192, March/April 2018.

Information

Published: March/April 2018
First available in Project Euclid: 19 December 2017

zbMATH: 1383.35206
MathSciNet: MR3738645

Subjects:
Primary: 35Q40, M35Q55

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.23 • No. 3/4 • March/April 2018
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