Global existence without decay for quadratic Klein-Gordon equations
Analysis of PDEs
2012-09-20 v2
Abstract
The Cauchy problem for quadratic Klein-Gordon systems is considered in two spatial dimensions and higher under a suitable non-resonance condition on the masses, including the main case of equal masses. A global well-posedness and scattering result is proven for small H^s data, s >= max(1/2, (n-2)/2), using the contraction mapping technique in U^2/V^2 based spaces. The result demonstrates that global results and scattering hold in this setting without the need to impose strong decay on the initial data.
Keywords
Cite
@article{arxiv.1209.1518,
title = {Global existence without decay for quadratic Klein-Gordon equations},
author = {Tobias Schottdorf},
journal= {arXiv preprint arXiv:1209.1518},
year = {2012}
}
Comments
22 pages