On Channels of Energy for the Radial Linearised Energy Critical Wave Equation in the Degenerate Case

Abstract

Abstract Channels of energy estimates control the energy of an initial data from that which it radiates outside a light cone. For the linearised energy critical wave equation, they have been obtained in the radial case in odd dimensions, first in three dimensions in [8], then for the general case in [10]. We consider even dimensions, for which such estimates are known to fail [2]. We propose a weaker version of these estimates, around a single ground state as well as around a multisoliton. This allows us in [1] to prove the soliton resolution conjecture in six dimensions.