Microlocal partition of energy for linear wave or Schrödinger equations

Jean-Marc Delort (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

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 non radial initial data.

Domaines: Equations aux dérivées partielles [math.AP]

Jean-Marc Delort. Microlocal partition of energy for linear wave or Schrödinger equations. 2021. ⟨hal-03227390v1⟩