Scattering for the Beam equation in low dimensions

Details Scattering for the Beam equation in low dimensions Scattering for the Beam equation in low dimensions

2009-03-23

arxiv.org/abs/0903.3777v2

Mathematics

Analysis of PDEs

23 pages, submitted. Proof of Proposition 1.2 corrected

Scientific paper

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.

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