Energy partition for the linear radial wave equation
Analysis of PDEs
2012-09-18 v1
Abstract
We consider the radial free wave equation in all dimensions and derive asymptotic formulas for the space partition of the energy relative to a light cone, as time goes to infinity. We show that the exterior energy estimate, which Duyckaerts, Merle and the second author obtained in odd dimensions, fails in even dimensions. Positive results for restricted classes of data are obtained. This is a companion paper to our two nonlinear papers with Andrew Lawrie.
Keywords
Cite
@article{arxiv.1209.3678,
title = {Energy partition for the linear radial wave equation},
author = {Raphael Cote and Carlos Kenig and Wilhelm Schlag},
journal= {arXiv preprint arXiv:1209.3678},
year = {2012}
}