Small data scattering of the inhomogeneous cubic–quintic NLS in 2 dimensions

Yonggeun Cho; Kiyeon Lee

doi:10.1016/j.na.2019.05.021

Small data scattering of the inhomogeneous cubic–quintic NLS in 2 dimensions

Yonggeun Cho^*
, Kiyeon Lee

^*Corresponding author for this work

Department of Mathematics

Jeonbuk National University

Research output: Contribution to journal › Journal article › peer-review

2 Scopus citations

Abstract

The aim of this paper is to show the small data scattering for 2D ICQNLS: iu_t=−Δu+K₁(x)|u|²u+K₂(x)|u|⁴u.Under the assumption that |∂^jK_l|≲|x|^b_l−j for j=0,1,2,l=1,2 and 0≤b_l≤l−2/3, we prove the small data scattering in an angularly regular Sobolev space H_θ ^1,1. We use the decaying property of angularly regular functions, which are defined as functions in Sobolev space H_θ ^1,1⊂H¹ with angular regularity such that ‖∂_θf‖_H¹<∞, and also use the recently developed angularly averaged Strichartz estimates (Tao, 2000; Cho and Lee, 2013; Guo et al., 2018). In addition, we suggest a sufficient condition for non-existence of scattering.

Original language	English
Pages (from-to)	142-157
Number of pages	16
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	188
DOIs	https://doi.org/10.1016/j.na.2019.05.021
State	Published - 2019.11

Keywords

2D inhomogeneous NLS
Angular regularity
Small data scattering

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1016/j.na.2019.05.021

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@article{4905db72f50e4ca293c006bc76268eeb,

title = "Small data scattering of the inhomogeneous cubic–quintic NLS in 2 dimensions",

abstract = "The aim of this paper is to show the small data scattering for 2D ICQNLS: iut=−Δu+K1(x)|u|2u+K2(x)|u|4u.Under the assumption that |∂jKl|≲|x|bl−j for j=0,1,2,l=1,2 and 0≤bl≤l−2/3, we prove the small data scattering in an angularly regular Sobolev space Hθ 1,1. We use the decaying property of angularly regular functions, which are defined as functions in Sobolev space Hθ 1,1⊂H1 with angular regularity such that ‖∂θf‖H1 <∞, and also use the recently developed angularly averaged Strichartz estimates (Tao, 2000; Cho and Lee, 2013; Guo et al., 2018). In addition, we suggest a sufficient condition for non-existence of scattering.",

keywords = "2D inhomogeneous NLS, Angular regularity, Small data scattering",

author = "Yonggeun Cho and Kiyeon Lee",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

year = "2019",

month = nov,

doi = "10.1016/j.na.2019.05.021",

language = "English",

volume = "188",

pages = "142--157",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

}

TY - JOUR

T1 - Small data scattering of the inhomogeneous cubic–quintic NLS in 2 dimensions

AU - Cho, Yonggeun

AU - Lee, Kiyeon

PY - 2019/11

Y1 - 2019/11

N2 - The aim of this paper is to show the small data scattering for 2D ICQNLS: iut=−Δu+K1(x)|u|2u+K2(x)|u|4u.Under the assumption that |∂jKl|≲|x|bl−j for j=0,1,2,l=1,2 and 0≤bl≤l−2/3, we prove the small data scattering in an angularly regular Sobolev space Hθ 1,1. We use the decaying property of angularly regular functions, which are defined as functions in Sobolev space Hθ 1,1⊂H1 with angular regularity such that ‖∂θf‖H1 <∞, and also use the recently developed angularly averaged Strichartz estimates (Tao, 2000; Cho and Lee, 2013; Guo et al., 2018). In addition, we suggest a sufficient condition for non-existence of scattering.

AB - The aim of this paper is to show the small data scattering for 2D ICQNLS: iut=−Δu+K1(x)|u|2u+K2(x)|u|4u.Under the assumption that |∂jKl|≲|x|bl−j for j=0,1,2,l=1,2 and 0≤bl≤l−2/3, we prove the small data scattering in an angularly regular Sobolev space Hθ 1,1. We use the decaying property of angularly regular functions, which are defined as functions in Sobolev space Hθ 1,1⊂H1 with angular regularity such that ‖∂θf‖H1 <∞, and also use the recently developed angularly averaged Strichartz estimates (Tao, 2000; Cho and Lee, 2013; Guo et al., 2018). In addition, we suggest a sufficient condition for non-existence of scattering.

KW - 2D inhomogeneous NLS

KW - Angular regularity

KW - Small data scattering

UR - https://www.scopus.com/pages/publications/85067075749

U2 - 10.1016/j.na.2019.05.021

DO - 10.1016/j.na.2019.05.021

M3 - Journal article

AN - SCOPUS:85067075749

SN - 0362-546X

VL - 188

SP - 142

EP - 157

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

ER -

Small data scattering of the inhomogeneous cubic–quintic NLS in 2 dimensions

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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