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

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

Abstract

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.

Original language	English
Journal	Electronic Journal of Differential Equations
Volume	2016
Publication status	Published - 2016 Jan 25

Keywords

Analytic smoothing effect
Global solution
Non elliptic Schrödinger equation
Nonlinear Schrödinger equation

ASJC Scopus subject areas

Analysis

Cite this

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title = "Analytic smoothing effect for the cubic hyperbolic schr{\"o}dinger equation in two space dimensions",

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.",

keywords = "Analytic smoothing effect, Global solution, Non elliptic Schr{\"o}dinger equation, Nonlinear Schr{\"o}dinger equation",

author = "Gaku Hoshino and Tohru Ozawa",

year = "2016",

month = jan,

day = "25",

language = "English",

volume = "2016",

journal = "Electronic Journal of Differential Equations",

issn = "1072-6691",

publisher = "Texas State University - San Marcos",

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T1 - Analytic smoothing effect for the cubic hyperbolic schrödinger equation in two space dimensions

AU - Hoshino, Gaku

AU - Ozawa, Tohru

PY - 2016/1/25

Y1 - 2016/1/25

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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M3 - Article

AN - SCOPUS:84955562979

SN - 1072-6691

SN - 1550-6150

VL - 2016

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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