Blow-up and scattering for the 1D NLS with point nonlinearity above the mass-energy threshold
Analysis of PDEs
2021-07-14 v1
Abstract
In this paper, we study the nonlinear Schr\"odinger equation with focusing point nonlinearity in dimension one. First, we establish a scattering criterion for the equation based on Kenig-Merle's compactness-rigidity argument. Then we prove the energy scattering below and above the mass-energy threshold. We also describe the dynamics of solutions with data at the ground state threshold. Finally, we prove a blow-up criteria for the equation with initial data with arbitrarily large energy.
Keywords
Cite
@article{arxiv.2106.09139,
title = {Blow-up and scattering for the 1D NLS with point nonlinearity above the mass-energy threshold},
author = {Alex H. Ardila},
journal= {arXiv preprint arXiv:2106.09139},
year = {2021}
}
Comments
30 pages