ILL-posedness for the quadratic nonlinear Schrödinger equation with nonlinearity μ2

Tsukasa Iwabuchi; Kota Uriya

doi:10.3934/cpaa.2015.14.1395

ILL-posedness for the quadratic nonlinear Schrödinger equation with nonlinearity μ²

Tsukasa Iwabuchi, Kota Uriya

SCI - Mathematics

Tohoku University

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

4 Citations (Scopus)

Abstract

We are concerned with the ill-posedness issue for the nonlinear Schrödinger equation with the quadratic nonlinearity μ² and prove the norm ination in the dimensions 1 ≤ n ≤ 3. This is the extension of the ill-posed result by Kishimoto-Tsugawa [12] in one dimension and also the remaining case of Iwabuchi-Ogawa [7].

Original language	English
Pages (from-to)	1395-1405
Number of pages	11
Journal	Communications on Pure and Applied Analysis
Volume	14
Issue number	4
DOIs	https://doi.org/10.3934/cpaa.2015.14.1395
Publication status	Published - 2015 Jul 1

Keywords

Ill-posedness
Nonlinear Schrödinger equation
Norm ination

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10.3934/cpaa.2015.14.1395

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abstract = "We are concerned with the ill-posedness issue for the nonlinear Schr{\"o}dinger equation with the quadratic nonlinearity μ2 and prove the norm ination in the dimensions 1 ≤ n ≤ 3. This is the extension of the ill-posed result by Kishimoto-Tsugawa [12] in one dimension and also the remaining case of Iwabuchi-Ogawa [7].",

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AU - Uriya, Kota

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KW - Nonlinear Schrödinger equation

KW - Norm ination

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ILL-posedness for the quadratic nonlinear Schrödinger equation with nonlinearity μ²

Abstract

Keywords

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