A P ] 7 A pr 2 00 5 Scattering theory for the Zakharov system

We study the theory of scattering for the Zakharov system in space dimension 3. We prove in particular the existence of wave operators for that system with no size restriction on the data in larger spaces and for more general asymptotic states than were previously considered, and we determine convergence rates in time of solutions in the range of the wave operators to the solutions of the underlying linear system. We also consider the same system in space dimension 2, where we prove the existence of wave operators for small Schrödinger data in the special case of vanishing asymptotic data for the wave field. AMS Classification : Primary 35P25. Secondary 35B40, 35Q60, 81U99.

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