Long range scattering for the Wave-Schrödinger system revisited
Résumé
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.