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

Abstract

Abstract We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions

$$D \ge 4$$

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.