Hörmander's method for the characteristic Cauchy problem and conformal scattering for a non linear wave equation

Abstract

The purpose of this note is to prove the existence of a conformal scattering operator for the cubic defocusing wave equation on a non-stationary background. The proof essentially relies on solving the characteristic initial value problem by the method developed by Hörmander. This method consists in slowing down the propagation speed of the waves to transform a characteristic initial value problem into a standard Cauchy problem.

References in corpus (3)

• Peeling of Dirac and Maxwell fields on a Schwarzschild background
• Conformal scattering for a nonlinear wave equation on a curved background
• Peeling on Kerr spacetime~:linear and non linear scalar fields

Cited by in corpus (5)

• Conformal scattering theory for the linearized gravity fields on Schwarzschild spacetime
• Conformal scattering theory for the Dirac field on Kerr spacetime
• Cauchy and Goursat problems for the generalized spin zero rest-mass fields on Minkowski spacetime
• Conformal Scattering of Maxwell Potentials
• Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime