Vol. 4, No. 2, 2022

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Microlocal partition of energy for linear wave or Schrödinger equations

Jean-Marc Delort

Vol. 4 (2022), No. 2, 329–385
Abstract

We prove a microlocal partition of energy for solutions to linear half-wave or Schrödinger equations in any space dimension. This extends well-known (local) results valid for the wave equation outside the wave cone, and allows us in particular, in the case of even dimension, to generalize the radial estimates due to Côte, Kenig and Schlag to nonradial initial data.

Keywords
wave equation, Schrödinger equation, channels of energy, microlocal analysis
Mathematical Subject Classification
Primary: 35L05
Secondary: 35Q41
Milestones
Received: 25 May 2021
Accepted: 6 January 2022
Published: 24 August 2022
Authors
Jean-Marc Delort
Département de Mathématiques
Université Paris XIII (Sorbonne Paris-Nord)
Villetaneuse
France