Scattering profile for global solutions of the energy-critical wave equation
Thomas Duyckaerts, Carlos Kenig, Frank Merle
TL;DR
This paper proves that global solutions of the focusing energy-critical wave equation in dimensions 3 to 5, which are bounded in energy, asymptotically resemble linear wave solutions outside wave cones.
Contribution
It establishes the scattering profile for bounded global solutions of the energy-critical wave equation in higher dimensions.
Findings
Global solutions converge to linear radiation outside wave cones.
Bounded energy solutions exhibit scattering behavior.
Results apply to dimensions 3, 4, and 5.
Abstract
Consider the focusing energy-critical wave equation in space dimension 3, 4 or 5. We prove that any global solution which is bounded in the energy space converges in the exterior of wave cones to a radiation term which is a solution of the linear wave equation.
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