Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach
Analysis of PDEs
2024-09-26 v2
Abstract
We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schr\"odinger equations (NLS) with mass-energy intercritical competing nonlinearities. Specifically, the NLS has a focusing leading order nonlinearity with a defocusing perturbation. Our strategy combines interaction Morawetz estimates \`a la Dodson-Murphy and a new crucial bound for the Pohozaev functional of localized functions, which is essential to overcome the lack of a monotonicity condition. Furthermore, we give the rate of blow-up for symmetric solutions.
Keywords
Cite
@article{arxiv.2209.01600,
title = {Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach},
author = {Jacopo Bellazzini and Van Duong Dinh and Luigi Forcella},
journal= {arXiv preprint arXiv:2209.01600},
year = {2024}
}
Comments
title slightly changed, abstract and introduction modified. 33 pages, no figures