Long range scattering for the Wave–Schrödinger system revisited

We reconsider the theory of scattering for the Wave–Schrödinger 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 Schrödinger...

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Bibliographic Details
Published in:Journal of Differential Equations 2012-01, Vol.252 (2), p.1642-1667
Main Authors: Ginibre, J., Velo, G.
Format: Article
Language:English
Subjects:
Long range scattering
Wave–Schrödinger system
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Summary:We reconsider the theory of scattering for the Wave–Schrödinger 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 Schrödinger asymptotic data and the Schrödinger solution in the treatment of that problem, in the special case of vanishing asymptotic data for the wave field.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2011.07.003