### 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 language | English |
---|---|

Pages (from-to) | 161-192 |

Number of pages | 32 |

Journal | Advances in Differential Equations |

Volume | 23 |

Issue number | 3-4 |

Publication status | Published - 2018 Mar 1 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Advances in Differential Equations*,

*23*(3-4), 161-192.

**On the focusing energy-critical fractional nonlinear schrödnger equations.** / Cho, Yonggeun; Hwang, Gyeongha; Ozawa, Tohru.

Research output: Contribution to journal › Article

*Advances in Differential Equations*, vol. 23, no. 3-4, pp. 161-192.

}

TY - JOUR

T1 - On the focusing energy-critical fractional nonlinear schrödnger equations

AU - Cho, Yonggeun

AU - Hwang, Gyeongha

AU - Ozawa, Tohru

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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].

AB - 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].

UR - http://www.scopus.com/inward/record.url?scp=85038360070&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038360070&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85038360070

VL - 23

SP - 161

EP - 192

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 3-4

ER -