Sharp Exponent of Stable Standing Waves for the Perturbated Hartree Equation
Analysis of PDEs
2026-03-27 v1
Abstract
This paper is concerned with the stability of standing waves for the mass-critical Hartree equation with a focusing perturbation by the variational method. The profile decomposition theory is employed to prove the attainability of the cross constrained variational problem, and then the comparison of two cross constrained variational problems is derived. The sharp criteria of blowup, the orbital stability, and strong instability of standing waves without any frequency constraint are obtained. This improves the cross constrained variational argument proposed by Zhang (2005).
Keywords
Cite
@article{arxiv.2603.24978,
title = {Sharp Exponent of Stable Standing Waves for the Perturbated Hartree Equation},
author = {Guoyi Fu and Shanshan Fu and Xiaoguang Li and Jian Zhang and Shihui Zhu},
journal= {arXiv preprint arXiv:2603.24978},
year = {2026}
}