Dynamics of Partial Differential Equations

Volume 2 (2005)

Number 2

Long range scattering and modified wave operators for the wave-Schrödinger system III

Pages: 101 – 125

DOI: https://dx.doi.org/10.4310/DPDE.2005.v2.n2.a1


J. Ginibre (Laboratoire de Physique Théorique, Université de Paris XI, Orsay, France)

G. Velo (Dipartimento di Fisica, Università di Bologna, Sezione di Bologna, Italy)


We continue the study of scattering theory for the system consisting of a Schrödinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In previous papers, we proved the existence of modified wave operators for that system with no size restriction on the data and we determined the asymptotic behaviour in time of solutions in the range of the wave operators, first under a support condition on the Schrödinger asymptotic state and then without that condition, but for solutions of relatively low regularity. Here we extend the latter result to the case of more regular solutions.


long range scattering, modified wave operators, wave-Schrödinger system

2010 Mathematics Subject Classification

Primary 35P25. Secondary 35B40, 35Q40, 81Uxx.

Published 1 January 2005