Dynamics of 3D focusing, energy-critical wave equation with radial data

Abstract: In this article we discuss the long-time dynamics of the radial solutions to the energy-critical wave equation in 3-dimensional space. We prove a quantitative version of soliton resolution result for solutions defined for all time $t>0$. The main tool is the radiation theory of wave equations and the major observation of this work is a correspondence between the radiation and the soliton collision behaviour of solutions.