Global dynamics below the ground states for NLS under partial harmonic confinement
Analysis of PDEs
2023-12-04 v1 Mathematical Physics
math.MP
Abstract
We are concerned with the global behavior of the solutions of the focusing mass supercritical nonlinear Schr{\"o}dinger equation under partial harmonic confinement. We establish a necessary and sufficient condition on the initial data below the ground states to determine the global behavior (blow-up/scattering) of the solution. Our proof of scattering is based on the varia-tional characterization of the ground states, localized virial estimates, linear profile decomposition and nonlinear profiles.
Keywords
Cite
@article{arxiv.2006.06205,
title = {Global dynamics below the ground states for NLS under partial harmonic confinement},
author = {Alex Ardila and Rémi Carles},
journal= {arXiv preprint arXiv:2006.06205},
year = {2023}
}
Comments
35 pages