Long range scattering for the Wave-Schrödinger system revisited

Details Long range scattering for the Wave-Schrödinger system revisited Long range scattering for the Wave-Schrödinger system revisited

2011-03-08

arxiv.org/abs/1103.1538v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

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.

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