Threshold solutions for the $3d$ cubic INLS: the energy-critical case
Analysis of PDEs
2026-01-12 v1
Abstract
We study the energy-critical cubic inhomogeneous NLS equation . In this work, we prove the existence of special solutions with energy equal to that of the ground state and use these solutions to characterize the behavior of solutions at the ground state energy. The singular factor in the nonlinearity significantly limits the smoothness of the ground state and prompts a novel approach to the modulation analysis.
Keywords
Cite
@article{arxiv.2601.05349,
title = {Threshold solutions for the $3d$ cubic INLS: the energy-critical case},
author = {Luccas Campos and Luiz Gustavo Farah and Jason Murphy},
journal= {arXiv preprint arXiv:2601.05349},
year = {2026}
}