Long Range Scattering and Modified Wave Operators for the Wave-Schr"odinger System III

Details Long Range Scattering and Modified Wave Operators for the Wave-Schr"odinger System III Long Range Scattering and Modified Wave Operators for the Wave-Schr"odinger System III

2005-03-24

arxiv.org/abs/math/0503551v1

Mathematics

Analysis of PDEs

latex 34 pages

Scientific paper

We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In previous papers, we proved the existence of modified wave operators for that system with no size restriction on the data and we determined the asymptotic behaviour in time of the solutions in the range of the wave operators, first under a support condition on the Schr"odinger asymptotic state and then without that condition, but for solutions of relatively low regularity. Here we extend the latter result to the case of more regular solutions.

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