H1 Scattering for Mass-Subcritical NLS with Short-Range Nonlinearity and Initial Data in Σ

N. Burq; V. Georgiev; N. Tzvetkov; N. Visciglia

doi:10.1007/s00023-022-01245-2

H¹ Scattering for Mass-Subcritical NLS with Short-Range Nonlinearity and Initial Data in Σ

N. Burq, V. Georgiev, N. Tzvetkov, N. Visciglia^*

^*この研究の対応する著者

大学院先進理工学研究科

研究成果: Article › 査読

抄録

We consider short-range mass-subcritical nonlinear Schrödinger equations, and we show that the corresponding solutions with initial data in Σ scatter in H¹. Hence we up-grade the classical scattering result proved by Yajima and Tsutsumi from L² to H¹. We also provide some partial results concerning the scattering of the first order moments, as well as a short proof via lens transform of a classical result due to Tsutsumi and Cazenave–Weissler on the scattering in Σ.

本文言語	English
ページ（範囲）	1355-1376
ページ数	22
ジャーナル	Annales Henri Poincare
巻	24
号	4
DOI	https://doi.org/10.1007/s00023-022-01245-2
出版ステータス	Published - 2023 4月

ASJC Scopus subject areas

統計物理学および非線形物理学
核物理学および高エネルギー物理学
数理物理学

文献へのアクセス

10.1007/s00023-022-01245-2

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引用スタイル

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title = "H1 Scattering for Mass-Subcritical NLS with Short-Range Nonlinearity and Initial Data in Σ",

abstract = "We consider short-range mass-subcritical nonlinear Schr{\"o}dinger equations, and we show that the corresponding solutions with initial data in Σ scatter in H1. Hence we up-grade the classical scattering result proved by Yajima and Tsutsumi from L2 to H1. We also provide some partial results concerning the scattering of the first order moments, as well as a short proof via lens transform of a classical result due to Tsutsumi and Cazenave–Weissler on the scattering in Σ.",

author = "N. Burq and V. Georgiev and N. Tzvetkov and N. Visciglia",

note = "Funding Information: N.T. was supported by ANR grant ODA (ANR-18-CE40-0020-01) and V.G. and N.V. by PRIN grant 2020XB3EFL; moreover, they acknowledge the Gruppo Nazionale per l{\textquoteright} Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni (GNAMPA) of the Istituzione Nazionale di Alta Matematica (INDAM). V.G. is also partially supported by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, and by Top Global University Project, Waseda University. Funding Information: Open access funding provided by Universit{\'a} di Pisa within the CRUI-CARE Agreement. Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2023",

month = apr,

doi = "10.1007/s00023-022-01245-2",

language = "English",

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journal = "Annales Henri Poincare",

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TY - JOUR

T1 - H1 Scattering for Mass-Subcritical NLS with Short-Range Nonlinearity and Initial Data in Σ

AU - Burq, N.

AU - Georgiev, V.

AU - Tzvetkov, N.

AU - Visciglia, N.

N1 - Funding Information: N.T. was supported by ANR grant ODA (ANR-18-CE40-0020-01) and V.G. and N.V. by PRIN grant 2020XB3EFL; moreover, they acknowledge the Gruppo Nazionale per l’ Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituzione Nazionale di Alta Matematica (INDAM). V.G. is also partially supported by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, and by Top Global University Project, Waseda University. Funding Information: Open access funding provided by Universitá di Pisa within the CRUI-CARE Agreement. Publisher Copyright: © 2022, The Author(s).

PY - 2023/4

Y1 - 2023/4

N2 - We consider short-range mass-subcritical nonlinear Schrödinger equations, and we show that the corresponding solutions with initial data in Σ scatter in H1. Hence we up-grade the classical scattering result proved by Yajima and Tsutsumi from L2 to H1. We also provide some partial results concerning the scattering of the first order moments, as well as a short proof via lens transform of a classical result due to Tsutsumi and Cazenave–Weissler on the scattering in Σ.

AB - We consider short-range mass-subcritical nonlinear Schrödinger equations, and we show that the corresponding solutions with initial data in Σ scatter in H1. Hence we up-grade the classical scattering result proved by Yajima and Tsutsumi from L2 to H1. We also provide some partial results concerning the scattering of the first order moments, as well as a short proof via lens transform of a classical result due to Tsutsumi and Cazenave–Weissler on the scattering in Σ.

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