A system of quadratic nonlinear Klein-Gordon equations in 2d

Nakao Hayashi; Pavel I. Naumkin

doi:10.1016/j.jde.2013.01.035

A system of quadratic nonlinear Klein-Gordon equations in 2d

Nakao Hayashi, Pavel I. Naumkin

Research Alliance Center for Mathematical Sciences (RACMaS)

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

2 Citations (Scopus)

Abstract

We consider the system of quadratic nonlinear Klein-Gordon equations in two space dimensions. Under the mass condition such that 2m₁>m₂, we construct the scattering operator in an almost natural weighted Sobolev class H^1+δ,1 or the scattering problem in lower order Sobolev class H_4/3-δ^1+δ∩H^1+δ, where δ>0 is small.

Original language	English
Pages (from-to)	3615-3646
Number of pages	32
Journal	Journal of Differential Equations
Volume	254
Issue number	8
DOIs	https://doi.org/10.1016/j.jde.2013.01.035
Publication status	Published - 2013 Apr 15

Keywords

Bilinear estimates
Nonlinear Klein-Gordon equations
Quadratic nonlinearity
Two space dimensions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2013.01.035

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abstract = "We consider the system of quadratic nonlinear Klein-Gordon equations in two space dimensions. Under the mass condition such that 2m1>m2, we construct the scattering operator in an almost natural weighted Sobolev class H1+δ,1 or the scattering problem in lower order Sobolev class H4/3-δ1+δ∩H1+δ, where δ>0 is small.",

keywords = "Bilinear estimates, Nonlinear Klein-Gordon equations, Quadratic nonlinearity, Two space dimensions",

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AU - Naumkin, Pavel I.

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AB - We consider the system of quadratic nonlinear Klein-Gordon equations in two space dimensions. Under the mass condition such that 2m1>m2, we construct the scattering operator in an almost natural weighted Sobolev class H1+δ,1 or the scattering problem in lower order Sobolev class H4/3-δ1+δ∩H1+δ, where δ>0 is small.

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KW - Nonlinear Klein-Gordon equations

KW - Quadratic nonlinearity

KW - Two space dimensions

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