Hokkaido Mathematical Journal

GINIBRE J., VELO G.,

Long range scattering for the Wave-Schr\"odinger system with large wave data and small Schr\"odinger data.

Hokkaido Mathematical Journal, 35 (2006) pp.261-287

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Abstract

We study the theory of scattering for the Wave-Schr\"odinger system with Yukawa type coupling in space dimension 3. We prove in particular the existence of modified wave operators for that system with no size restriction on the wave data in the framework of a direct method which requires smallness of the Schr\"odinger data, and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.

MSC(Primary)81U99
MSC(Secondary)35Q40, 35P25, 35B40
Uncontrolled Keywordslong range scattering, modified wave operators, Wave-Schr\"odinger system