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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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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: http://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.