@inproceedings{1e0fdf9a464c47c89ac337d11042a88f,
title = "Orbital stability of standing waves for fractional hartree equation with unbounded potentials",
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.",
keywords = "Fractional Hartree equation, Orbital stability, Standing wave",
author = "Jian Zhang and Shijun Zheng and Shihui Zhu",
note = "Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.; AMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations and PDE Analysis on Fluid Flows, 2017 ; Conference date: 05-01-2017 Through 07-01-2017",
year = "2019",
doi = "10.1090/conm/725/14561",
language = "English",
isbn = "9781470441098",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "265--275",
editor = "Shijun Zheng and Jerry Bona and Geng Chen and {Van Phan}, Tuoc and Marius Beceanu and Avy Soffer",
booktitle = "Nonlinear Dispersive Waves and Fluids",
address = "United States",
}