IUMJ

Title: Scattering for the defocusing Beam equation in low dimensions

Authors: Benoit Pausader

Issue: Volume 59 (2010), Issue 3, 791-822

Abstract:

In this paper, we prove scattering for the defocusing Beam equation $\partial_t^2 u + \Delta^2 u + mu + \lambda|u|^{p-1}u =0$ in low dimensions $2 \le n \le 4$ for $p > 1 + 8/n$ and $\lambda > 0$. 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 derived from concentration-compactness ideas, and the latter by considering a Virial-type identity in the direction orthogonal to the Momentum vector.