Orbital stability of standing waves for fractional hartree equation with unbounded potentials

Jian Zhang, Shijun Zheng, Shihui Zhu

Research output: Contribution to book or proceedingConference articlepeer-review

5 Scopus citations

Abstract

We prove the existence of the set of ground states in a suitable energy space Σs = {u: RN ū(−Δ + m2 )s u + V |u|2 < ∞}, s ∈ (0,N2) for the mass-subcritical nonlinear fractional Hartree equation with unbounded potentials. As a consequence we obtain, as a priori result, the orbital stability of the set of standing waves. The main ingredient is the observation that Σs is compactly embedded in L2 . This enables us to apply the concentration compactness argument in the works of Cazenave-Lions and Zhang, namely, relative compactness for any minimizing sequence in the energy space.

Original languageEnglish
Title of host publicationNonlinear Dispersive Waves and Fluids
EditorsShijun Zheng, Jerry Bona, Geng Chen, Tuoc Van Phan, Marius Beceanu, Avy Soffer
PublisherAmerican Mathematical Society
Pages265-275
Number of pages11
ISBN (Print)9781470441098
DOIs
StatePublished - 2019
EventAMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations and PDE Analysis on Fluid Flows, 2017 - Atlanta, United States
Duration: Jan 5 2017Jan 7 2017

Publication series

NameContemporary Mathematics
Volume725
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

ConferenceAMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations and PDE Analysis on Fluid Flows, 2017
Country/TerritoryUnited States
CityAtlanta
Period01/5/1701/7/17

Scopus Subject Areas

  • General Mathematics

Keywords

  • Fractional Hartree equation
  • Orbital stability
  • Standing wave

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