## Advanced Studies in Pure Mathematics

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

Hironobu Sasaki

#### 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

Dates
Revised: 10 January 2006
First available in Project Euclid: 16 December 2018