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Global dynamics below the ground state for the focusing Schrödinger equation with a potential

Global dynamics below the ground state for the focusing Schrödinger equation with a potential J. Evol. Equ. Journal of Evolution © 2019 Springer Nature Switzerland AG Equations https://doi.org/10.1007/s00028-019-00547-z Global dynamics below the ground state for the focusing Schrödinger equation with a potential Masaru Hamano and Masahiro Ikeda Abstract. In this paper, we consider the nonlinear Schrödinger equation with a real-valued potential V = V (x ). We study global behavior of solutions to the equation with data below the ground state under some conditions for the potential V and prove a scattering result and a blowing-up result in mass-supercritical and energy-subcritical. Our proof of the scattering result is based on an argument by Dodson–Murphy (Proc Am Math Soc 145(11):4859–4867, 2017). The proof of the blowing-up or growing-up result without radially symmetric assumption is based on the argument by Du–Wu–Zhang (Discrete Contin Dyn Syst 36(7):3639– 3650, 2016). We can exclude the possibility of the growing-up result by the argument (Inui et al. in Blow-up of the radially symmetric solutions for the quadratic nonlinear Schrodinger system without mass resonance, arXiv:1810.09153.; Nakanishi and Schlag in Calc Var Partial Differ Eq 44(1-2):1–45, 2012; Glassey in J Math Phys 18(9):1794–1797, 1977) if “the data and the potential are radially symmetric” or “the data has finite variance.” Contents 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Global dynamics below the ground state for the focusing Schrödinger equation with a potential

Hamano, Masaru; Ikeda, Masahiro
Journal of Evolution Equations , Volume OnlineFirst – Oct 30, 2019
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References (35)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Nature Switzerland AG
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-019-00547-z
Publisher site
See Article on Publisher Site

Abstract

J. Evol. Equ. Journal of Evolution © 2019 Springer Nature Switzerland AG Equations https://doi.org/10.1007/s00028-019-00547-z Global dynamics below the ground state for the focusing Schrödinger equation with a potential Masaru Hamano and Masahiro Ikeda Abstract. In this paper, we consider the nonlinear Schrödinger equation with a real-valued potential V = V (x ). We study global behavior of solutions to the equation with data below the ground state under some conditions for the potential V and prove a scattering result and a blowing-up result in mass-supercritical and energy-subcritical. Our proof of the scattering result is based on an argument by Dodson–Murphy (Proc Am Math Soc 145(11):4859–4867, 2017). The proof of the blowing-up or growing-up result without radially symmetric assumption is based on the argument by Du–Wu–Zhang (Discrete Contin Dyn Syst 36(7):3639– 3650, 2016). We can exclude the possibility of the growing-up result by the argument (Inui et al. in Blow-up of the radially symmetric solutions for the quadratic nonlinear Schrodinger system without mass resonance, arXiv:1810.09153.; Nakanishi and Schlag in Calc Var Partial Differ Eq 44(1-2):1–45, 2012; Glassey in J Math Phys 18(9):1794–1797, 1977) if “the data and the potential are radially symmetric” or “the data has finite variance.” Contents 1.

Journal

Journal of Evolution Equations – Springer Journals

Published: Oct 30, 2019

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