A sharp scattering threshold level for mass-subcritical nonlinear Schr\"odinger system
Analysis of PDEs
2020-01-01 v1
Abstract
In this paper, we consider the quadratic nonlinear Schr\"odinger system in three space dimensions. Our aim is to obtain sharp scattering criteria. Because of the mass-subcritical nature, it is difficult to do so in terms of conserved quantities. The corresponding single equation is studied by the second author and a sharp scattering criteria is established by introducing a distance from a trivial scattering solution, the zero solution. By the structure of the nonlinearity we are dealing with, the system admits a scattering solution which is a pair of zero solution and a linear solution. Taking this fact into account, we introduce a new optimizing quantity and give a sharp scattering criterion in terms of it.
Cite
@article{arxiv.1912.12584,
title = {A sharp scattering threshold level for mass-subcritical nonlinear Schr\"odinger system},
author = {Masaru Hamano and Satoshi Masaki},
journal= {arXiv preprint arXiv:1912.12584},
year = {2020}
}
Comments
28 pages