Scattering for the Beam equation in low dimensions
Analysis of PDEs
2009-04-21 v2
Abstract
In this paper, we prove scattering for the defocusing Beam equation u_{tt}+D^2u+mu+ |u|^{p-1}u=0 in the energy space in low dimensions 1< n <5 for p>1+8/n. The main difficulty is the absence of a Morawetz-type estimate and of a Galilean transformation in order to be able to control the Momentum vector. We overcome the former by using a strategy of Kenig and Merle derived from concentration-compactness ideas, and the latter by considering a Virial-type identity in the direction orthogonal to the Momentum vector.
Cite
@article{arxiv.0903.3777,
title = {Scattering for the Beam equation in low dimensions},
author = {Benoit Pausader},
journal= {arXiv preprint arXiv:0903.3777},
year = {2009}
}
Comments
23 pages, submitted. Proof of Proposition 1.2 corrected