Global well-posedness and scattering for mass-critical, defocusing, infinite dimensional vector-valued resonant nonlinear Schrödinger system

Abstract

In this article, we consider the infinite dimensional vector-valued resonant nonlinear Schrödinger system, which arises from the study of the asymptotic behavior of the defocusing nonlinear Schrödinger equation on "wave guide" manifolds like ${\mathbb{R}}^2\times \mathbb{T}$ in [7]. We show global well-posedness and scattering for this system by long time Strichartz estimates and frequency localized interaction Morawetz estimates. As a by-product, our results make the arguments of scattering theory in [7] closed as crucial ingredients for compactness of the critical elements.

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Cited by in corpus (2)

• On scattering for the defocusing quintic nonlinear Schrödinger equation on the two-dimensional cylinder
• On the decay property of the cubic fourth-order Schrödinger equation