Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions
Analysis of PDEs
2017-03-16 v1
Abstract
In this paper, we consider the final state problem for the nonlinear Klein-Gordon equation (NLKG) with a critical nonlinearity in three space dimensions. We prove that for a given asymptotic profile, there exists a solution to (NLKG) which converges to given asymptotic profile as t to infinity. Here the asymptotic profile is given by the leading term of the solution to the linear Klein-Gordon equation with a logarithmic phase correction. Construction of a suitable approximate solution is based on the combination of Fourier series expansion for the nonlinearity used in our previous paper and smooth modification of phase correction by Ginibre-Ozawa.
Keywords
Cite
@article{arxiv.1703.04888,
title = {Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions},
author = {Satoshi Masaki and Jun-ichi Segata},
journal= {arXiv preprint arXiv:1703.04888},
year = {2017}
}