Ill-posedness for a system of quadratic nonlinear Schrödinger equations in two dimensions

Tsukasa Iwabuchi; Takayoshi Ogawa; Kota Uriya

doi:10.1016/j.jfa.2016.04.017

Ill-posedness for a system of quadratic nonlinear Schrödinger equations in two dimensions

Tsukasa Iwabuchi, Takayoshi Ogawa, Kota Uriya

SCI - Mathematics

Tohoku University

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

This paper concerns the ill-posedness issue for a system of quadratic nonlinear Schrödinger equations in two dimensions. From previous studies for the large time behavior of the solution to the system, one may expect that the critical regularity to show the well-posedness depends on the dispersion coefficients. To prove the ill-posedness, we show the failure of the uniform continuity of the data-solution map for the mass resonance case and show the norm inflation for other cases.

Original language	English
Pages (from-to)	136-163
Number of pages	28
Journal	Journal of Functional Analysis
Volume	271
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2016.04.017
Publication status	Published - 2016 Jul 1

Keywords

Ill-posedness
Mass resonance
Norm inflation
System of nonlinear Schrödinger equations

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title = "Ill-posedness for a system of quadratic nonlinear Schr{\"o}dinger equations in two dimensions",

abstract = "This paper concerns the ill-posedness issue for a system of quadratic nonlinear Schr{\"o}dinger equations in two dimensions. From previous studies for the large time behavior of the solution to the system, one may expect that the critical regularity to show the well-posedness depends on the dispersion coefficients. To prove the ill-posedness, we show the failure of the uniform continuity of the data-solution map for the mass resonance case and show the norm inflation for other cases.",

keywords = "Ill-posedness, Mass resonance, Norm inflation, System of nonlinear Schr{\"o}dinger equations",

author = "Tsukasa Iwabuchi and Takayoshi Ogawa and Kota Uriya",

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AU - Uriya, Kota

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N2 - This paper concerns the ill-posedness issue for a system of quadratic nonlinear Schrödinger equations in two dimensions. From previous studies for the large time behavior of the solution to the system, one may expect that the critical regularity to show the well-posedness depends on the dispersion coefficients. To prove the ill-posedness, we show the failure of the uniform continuity of the data-solution map for the mass resonance case and show the norm inflation for other cases.

AB - This paper concerns the ill-posedness issue for a system of quadratic nonlinear Schrödinger equations in two dimensions. From previous studies for the large time behavior of the solution to the system, one may expect that the critical regularity to show the well-posedness depends on the dispersion coefficients. To prove the ill-posedness, we show the failure of the uniform continuity of the data-solution map for the mass resonance case and show the norm inflation for other cases.

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Ill-posedness for a system of quadratic nonlinear Schrödinger equations in two dimensions

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