Scattering theory for the Zakharov system

J. Ginibre (1) , G. Velo

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

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 in the special case of vanishing asymptotic data for the wave field.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Algèbres quantiques [math.QA]

J. Ginibre, G. Velo. Scattering theory for the Zakharov system. Hokkaido Mathematical Journal, 2006, 35, pp.865-892. ⟨hal-00013348⟩