Scattering for the defocusing Beam equation in low dimensions Benoit Pausader 35Q74fourth-order wave equationsnonlinear beam equationsscattering 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. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.3966 10.1512/iumj.2010.59.3966 en Indiana Univ. Math. J. 59 (2010) 791 - 822 state-of-the-art mathematics http://iumj.org/access/