Profile decomposition and scattering for general nonlinear Schr{\"o}dinger equations
Analysis of PDEs
2024-02-13 v2
Abstract
We consider a Schr{\"o}dinger equation with a nonlinearity which is a general perturbation of a power'' nonlinearity. We construct a profile decomposition adapted to this nonlinearity.We also prove global existence and scattering in a general defocusing setting, assuming thatthe critical Sobolev norm is bounded in the energy-supercritical case. This generalizes severalprevious works on double-power nonlinearities.
Keywords
Cite
@article{arxiv.2401.10939,
title = {Profile decomposition and scattering for general nonlinear Schr{\"o}dinger equations},
author = {Thomas Duyckaerts and Phan van Tin},
journal= {arXiv preprint arXiv:2401.10939},
year = {2024}
}