Qualitative study of the critical wave equation with a subcritical perturbation

The goal of this work is the high frequency approximation of bounded energy solutions to the equation (E)□u+|u|4u+|u|α−1u=0,(t,x)∈Rt×Rx3, where □=∂t2−▵x is the wave operator and α is a real number, 1<α<5. We prove that the description of Bahouri and Gérard [Amer. J. Math. 121 (1999) 131-175] about the critical case still holds for Eq. (E) locally in time.