Energy partition for the linear radial wave equation

Raphaël Côte (1) , Carlos Kenig (2) , Wilhelm Schlag (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 Department of Mathematics

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.

Mots clés: linear wave equation; partition of the energy; exterior cone; concentration compactness; profile decomposition

Domaines: Equations aux dérivées partielles [math.AP]

Raphaël Côte, Carlos Kenig, Wilhelm Schlag. Energy partition for the linear radial wave equation. Mathematische Annalen, 2014, 358 (3-4), pp.573-607. ⟨10.1007/s00208-013-0970-x⟩. ⟨hal-00832749⟩