Analytic smoothing effect for the cubic hyperbolic schrödinger equation in two space dimensions

Gaku Hoshino; Tohru Ozawa

Analytic smoothing effect for the cubic hyperbolic schrödinger equation in two space dimensions

研究成果: Article

抜粋

We study the Cauchy problem for the cubic hyperbolic Schrödinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.

元の言語	English
ジャーナル	Electronic Journal of Differential Equations
巻	2016
出版物ステータス	Published - 2016 1 25

ASJC Scopus subject areas

Analysis

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これを引用

Hoshino, G., & Ozawa, T. (2016). Analytic smoothing effect for the cubic hyperbolic schrödinger equation in two space dimensions. Electronic Journal of Differential Equations, 2016.

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abstract = "We study the Cauchy problem for the cubic hyperbolic Schr{\"o}dinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.",

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AU - Ozawa, Tohru

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N2 - We study the Cauchy problem for the cubic hyperbolic Schrödinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.

AB - We study the Cauchy problem for the cubic hyperbolic Schrödinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.

KW - Analytic smoothing effect

KW - Global solution

KW - Non elliptic Schrödinger equation

KW - Nonlinear Schrödinger equation

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JO - Electronic Journal of Differential Equations

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