Channels of energy for the linear radial wave equation
Carlos Kenig, Andrew Lawrie, Baoping Liu, Wilhelm Schlag
TL;DR
This paper derives the general form of exterior channel of energy estimates for the radial wave equation in all odd dimensions, which is crucial for analyzing soliton resolution in equivariant wave maps.
Contribution
It extends the known channel of energy estimates to all odd dimensions for the radial free wave equation, enabling broader applications.
Findings
Derived general form of energy channels in all odd dimensions
Established foundation for soliton resolution in wave maps
Extended previous 3D and 5D results to all odd dimensions
Abstract
Exterior channel of energy estimates for the radial wave equation were first considered in three dimensions by Duyckaerts, the first author, and Merle, and recently for the 5-dimensional case by the first, second, and fourth authors. In this paper we find the general form of the channel of energy estimate in all odd dimensions for the radial free wave equation. This will be used in a companion paper to establish soliton resolution for equivariant wave maps in 3 dimensions exterior to the ball B(0,1), and in all equivariance classes.
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