Hörmander’s method for the characteristic Cauchy problem and conformal 
scattering for a nonlinear wave equation

Joudioux, Jérémie

doi:10.1007/s11005-020-01266-0

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Hörmander’s method for the characteristic Cauchy problem and conformal scattering for a nonlinear wave equation

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Joudioux, Jérémie
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Joudioux, J. (2020). Hörmander’s method for the characteristic Cauchy problem and conformal scattering for a nonlinear wave equation. Letters in Mathematical Physics, 110(6), 1391-1423. doi:10.1007/s11005-020-01266-0.

Cite as: https://hdl.handle.net/21.11116/0000-0003-484A-A

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 H\"ormander. This method consists in slowing
down the propagation speed of the waves to transform a characteristic initial
value problem into a standard Cauchy problem.