PUB - Publikationen an der Universität Bielefeld

We consider the final-state problem for the Zakharov system in the energy space in three space dimensions. For (u(+),v(+))is an element of H(1)xL(2) without any size restriction, symmetry assumption or additional angular regularity, we perform a physical-space randomization on u+ and an angular randomization on v(+) yielding random final states (u(+)(omega),v(+)(omega)). We obtain that for almost every omega, there is a unique solution of the Zakharov system scattering to the final state (u(+)(omega),v(+)(omega)). The key ingredient in the proof is the use of time-weighted norms and generalized Strichartz estimates which are accessible due to the randomization.