Well-posedness and scattering of inhomogeneous cubic-quintic NLS

Yonggeun Cho

doi:10.1063/1.5053131

Well-posedness and scattering of inhomogeneous cubic-quintic NLS

Yonggeun Cho^*

^*Corresponding author for this work

Department of Mathematics

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

3 Scopus citations

Abstract

In this paper, we consider inhomogeneous cubic-quintic nonlinear Schrödinger (ICQNLS) in space dimension d = 3, iu_t = -Δu + K₁(x)|u|²u + K₂(x)|u|⁴u. We study local well-posedness, finite time blowup, and small data scattering and nonscattering for the ICQNLS when K1,K2-C4(R3\{0}) satisfy growth condition |jKi(x)|x|bi-j (j=0,1,2,3,4) for some b_i ≥ 0 and for x 0. To this end, we use the Sobolev inequality for the functions f Hⁿ (n = 1, 2) such that -|L|-Hn<∞ (=1,2), where L is the angular momentum operator defined by L = x × (-i).

Original language	English
Article number	081513
Journal	Journal of Mathematical Physics
Volume	60
Issue number	8
DOIs	https://doi.org/10.1063/1.5053131
State	Published - 2019.08.1

Quacquarelli Symonds(QS) Subject Topics

Physics & Astronomy

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10.1063/1.5053131

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@article{71da809d6175412d9f04da9ae74b57af,

title = "Well-posedness and scattering of inhomogeneous cubic-quintic NLS",

abstract = "In this paper, we consider inhomogeneous cubic-quintic nonlinear Schr{\"o}dinger (ICQNLS) in space dimension d = 3, iut = -Δu + K1(x)|u|2u + K2(x)|u|4u. We study local well-posedness, finite time blowup, and small data scattering and nonscattering for the ICQNLS when K1,K2-C4(R3\textbackslash{}\{0\}) satisfy growth condition |jKi(x)|x|bi-j (j=0,1,2,3,4) for some bi ≥ 0 and for x 0. To this end, we use the Sobolev inequality for the functions f Hn (n = 1, 2) such that -|L|-Hn<∞ (=1,2), where L is the angular momentum operator defined by L = x × (-i).",

author = "Yonggeun Cho",

note = "Publisher Copyright: {\textcopyright} 2019 Author(s).",

year = "2019",

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doi = "10.1063/1.5053131",

language = "English",

volume = "60",

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T1 - Well-posedness and scattering of inhomogeneous cubic-quintic NLS

AU - Cho, Yonggeun

PY - 2019/8/1

Y1 - 2019/8/1

N2 - In this paper, we consider inhomogeneous cubic-quintic nonlinear Schrödinger (ICQNLS) in space dimension d = 3, iut = -Δu + K1(x)|u|2u + K2(x)|u|4u. We study local well-posedness, finite time blowup, and small data scattering and nonscattering for the ICQNLS when K1,K2-C4(R3\{0}) satisfy growth condition |jKi(x)|x|bi-j (j=0,1,2,3,4) for some bi ≥ 0 and for x 0. To this end, we use the Sobolev inequality for the functions f Hn (n = 1, 2) such that -|L|-Hn<∞ (=1,2), where L is the angular momentum operator defined by L = x × (-i).

AB - In this paper, we consider inhomogeneous cubic-quintic nonlinear Schrödinger (ICQNLS) in space dimension d = 3, iut = -Δu + K1(x)|u|2u + K2(x)|u|4u. We study local well-posedness, finite time blowup, and small data scattering and nonscattering for the ICQNLS when K1,K2-C4(R3\{0}) satisfy growth condition |jKi(x)|x|bi-j (j=0,1,2,3,4) for some bi ≥ 0 and for x 0. To this end, we use the Sobolev inequality for the functions f Hn (n = 1, 2) such that -|L|-Hn<∞ (=1,2), where L is the angular momentum operator defined by L = x × (-i).

UR - https://www.scopus.com/pages/publications/85072016646

U2 - 10.1063/1.5053131

DO - 10.1063/1.5053131

M3 - Journal article

AN - SCOPUS:85072016646

SN - 0022-2488

VL - 60

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 8

M1 - 081513

ER -

Well-posedness and scattering of inhomogeneous cubic-quintic NLS

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