Blow-up solutions for a system of Schr\"{o}dinger equations with general quadratic-type nonlinearities in dimensions five and six
Analysis of PDEs
2020-03-26 v1
Abstract
In this work, we show the existence of ground state solutions for an -component system of non-linear Schr\"{o}dinger equations with quadratic-type growth interactions in the energy-critical case. They are obtained analyzing a critical Sobolev-type inequality and using the concentration-compactness method. As an application, we prove the existence of blow-up solutions of the system without the mass-resonance condition in dimension six (and five), when the initial data is radial.
Keywords
Cite
@article{arxiv.2003.11103,
title = {Blow-up solutions for a system of Schr\"{o}dinger equations with general quadratic-type nonlinearities in dimensions five and six},
author = {Norman Noguera and Ademir Pastor},
journal= {arXiv preprint arXiv:2003.11103},
year = {2020}
}