Scattering and Blow-Up in Both Time Directions Above the Ground State for the Focusing Nonlinear Schr\'{o}dinger Equation

Autor:	Miller, Ian
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs 35A01 35B44 35Q55 35Q60
Druh dokumentu:	Working Paper
Popis:	In this article we obtain new scattering and blow-up solutions for intercritical focusing nonlinear Schr\"{o}dinger equations (NLS) above the ground state mass-energy threshold. The main focus of this article is the establishment of some solutions with arbitrarily large mass-energy which scatter in both time directions. In particular, large mass-energy which does not arise from the Galilean transformation. We additionally obtain new criteria for blow-up in both time directions, as well as improved sufficient conditions for scattering and blow-up in one time direction. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.06962 Zobrazit plný text záznamu View this record from Arxiv