Small data blow-up for a system of nonlinear Schrödinger equations

Tohru Ozawa; Hideaki Sunagawa

doi:10.1016/j.jmaa.2012.10.003

Small data blow-up for a system of nonlinear Schrödinger equations

Tohru Ozawa, Hideaki Sunagawa^*

^*この研究の対応する著者

先進理工学部

研究成果: Article › 査読

22 被引用数 (Scopus)

抄録

We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrödinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.

本文言語	English
ページ（範囲）	147-155
ページ数	9
ジャーナル	Journal of Mathematical Analysis and Applications
巻	399
号	1
DOI	https://doi.org/10.1016/j.jmaa.2012.10.003
出版ステータス	Published - 2013 3月 1

ASJC Scopus subject areas

分析
応用数学

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10.1016/j.jmaa.2012.10.003

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abstract = "We give examples of small data blow-up for a three-component system of quadratic nonlinear Schr{\"o}dinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.",

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AB - We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrödinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.

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KW - Mass resonance

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KW - Small data blow-up

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Small data blow-up for a system of nonlinear Schrödinger equations

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