High frequency approximation of solutions to critical nonlinear wave equations

This work is devoted to the description of bounded energy sequences of solu tions to the equation (1) square u + \u\(4) = 0 in R x R-3, up to remainder terms small in energy norm and in every Strichartz norm. The proof relies on scattering theory for (1) and on a structure theorem for bounded energy sequences of solutions to the linear wave equation. In particular, we infer the existence of an a priori estimate of Strichartz norms of solutions to (1) in terms of their energy.