Qualitative analysis of energy ground states for magnetic focusing Gross-Pitaevskii equations
Abstract
We prove the uniqueness, asymptotics, symmetry, and orbital stability of energy ground states for 3D magnetic Gross-Pitaevskii equations under mild conditions on the electric potential and magnetic field. In particular, both the electric potential and the magnetic field are allowed to have singularities, and we cover in a unified approach the physically relevant Aharonov-Bohm magnetic field as well as the constant magnetic field. Since we are in the 3D case, the unique energy ground state (up to a phase factor) is obtained as a local minimizer, rather than a global one, by restricting the kinetic energy of candidate critical points within a suitable range. The qualitative analysis of the energy ground state we carry on is mainly based on a related Pohozaev identity, the implicit function theorem, and variational methods.
Related
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- Global well-posedness for the energy-critical focusing NLS on 𝕋3
BibTeX
@misc{an2026qualitative,
title = {{Qualitative analysis of energy ground states for magnetic focusing Gross-Pitaevskii equations}},
author = {Xiaoming An and Lun Guo and Xiao Luo and Riccardo Molle},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28392},
eprint = {2608.28392},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28392},
}
RIS
TY - UNPB
TI - Qualitative analysis of energy ground states for magnetic focusing Gross-Pitaevskii equations
AU - Xiaoming An
AU - Lun Guo
AU - Xiao Luo
AU - Riccardo Molle
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28392
UR - https://arxiv.org/abs/2608.28392
AB - We prove the uniqueness, asymptotics, symmetry, and orbital stability of energy ground states for 3D magnetic Gross-Pitaevskii equations under mild conditions on the electric potential and magnetic field. In particular, both the electric potential and the magnetic field are allowed to have singularities, and we cover in a unified approach the physically relevant Aharonov-Bohm magnetic field as well as the constant magnetic field. Since we are in the 3D case, the unique energy ground state (up to a phase factor) is obtained as a local minimizer, rather than a global one, by restricting the kinetic energy of candidate critical points within a suitable range. The qualitative analysis of the energy ground state we carry on is mainly based on a related Pohozaev identity, the implicit function theorem, and variational methods.
ER -