Weighted energy decay for magnetic Klein–Gordon equation

Abstract

We obtain a dispersion long-time decay in weighted energy norms for solutions of 3D Klein–Gordon equation with magnetic and scalar potentials. The decay extends the results obtained by Jensen and Kato for the Schrödinger equation with scalar potential. For the proof we develop the spectral theory of Agmon, Jensen and Kato, and minimal escape velocities estimates of Hunziker, Sigal and Soffer.

Keywords:

• dispersion decay
• weighted energy norms
• magnetic Klein–Gordon equation
• resolvent

AMS Subject Classifications:

• 35L10
• 34L25
• 47A40
• 81U05