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Long range scattering for the Wave-Schr\"odinger system revisited

By Jean Ginibre and Giorgio Velo

Abstract

We reconsider the theory of scattering for the Wave-Schr\"odinger system and more precisely the local Cauchy problem with infinite initial time, which is the main step in the construction of the wave operators. Using a method due to Nakanishi, we eliminate a loss of regularity between the Schr\"odinger asymptotic data and the Schr\"odinger solution in the treatment of that problem, in the special case of vanishing asymptotic data for the wave field.Comment: 32 page

Topics: Mathematics - Analysis of PDEs, Mathematical Physics, Primary 35P25. Secondary 35B40, 35Q40, 81U99
Year: 2011
OAI identifier: oai:arXiv.org:1103.1538
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