骆泳铭,深圳北理莫斯科大学

We consider the Cauchy problem for the defocusing cubic NLS on R3T1 and establish almost sure scattering for random initial data. The main obstacle to extend the classical almost sure scattering results established for the Euclidean spaces to the waveguide manifolds is that the smoothing effect obtained from randomizing the initial data is unavailable for bounded domains. To overcome this difficulty, we exploit a layer-by-layer refinement of the newly established randomization introduced by Shen-Soffer-Wu, which enables us to also obtain strongly smoothing effect from the randomization for the forcing term along the periodic direction. Particularly, we assume no symmetry conditions and the almost sure scattering result is available for arbitrarily rough data.