Advanced Studies in Pure Mathematics

Small data scattering for the Klein-Gordon equation with a cubic convolution

Hironobu Sasaki

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Abstract

We consider the scattering problem for the Klein-Gordon equation with cubic convolution nonlinearity. We present the method to prove the existence of the scattering operator on a neighborhood of 0 in the weighted Sobolev space $H^{s,\sigma} = (1- \Delta)^{-s/2}\ \langle x \rangle^{-\sigma}\ L_2 (\mathbb{R}^n)$. The method is based on the complex interpolation method of the weighted Sobolev spaces and the Strichartz estimates for the inhomogeneous Klein-Gordon equation.

Article information

Source
Asymptotic Analysis and Singularities — Hyperbolic and dispersive PDEs and fluid mechanics, H. Kozono, T. Ogawa, K. Tanaka, Y. Tsutsumi and E. Yanagida, eds. (Tokyo: Mathematical Society of Japan, 2007), 321-328

Dates
Received: 31 October 2005
Revised: 10 January 2006
First available in Project Euclid: 16 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1545000600

Digital Object Identifier
doi:10.2969/aspm/04710321

Mathematical Reviews number (MathSciNet)
MR2387241

Citation

Sasaki, Hironobu. Small data scattering for the Klein-Gordon equation with a cubic convolution. Asymptotic Analysis and Singularities — Hyperbolic and dispersive PDEs and fluid mechanics, 321--328, Mathematical Society of Japan, Tokyo, Japan, 2007. doi:10.2969/aspm/04710321. https://projecteuclid.org/euclid.aspm/1545000600


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