Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case

We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions D ≥ 4 . This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution W , called the ground state. We prove that every finite energy solution with bounded energy norm resolves, continuously in time, into a finite superposition of asymptotically decoupled copies of the ground state and free radiation.