PROFILES FOR THE RADIAL FOCUSING ENERGY-CRITICAL WAVE EQUATION IN ODD DIMENSIONS

In this paper, we consider global and non-global radial solutions of the focusing energy-critical wave equation on R x R-N where N >= 5 is odd. We prove that if the solution remains bounded in the energy space as you approach the maximal forward time of existence, then along a sequence of times converging to the maximal forward time of existence, the solution decouples into a sum of dynamically resealed solitons, a free radiation term, and an error tending to zero in the energy space. If, in addition, we assume a bound on the evolution that rules out the formation of multiple solitons, then this decoupling holds for all times approaching the maximal forward time of existence.