On scattering for the quintic defocusing nonlinear Schrödinger equation on \R \times \T^2

Abstract

We consider the problem of large data scattering for the quintic nonlinear Schrödinger equation on $\R \times \T^2$. This equation is critical both at the level of energy and mass. Most notably, we exhibit a new type of profile (a "large scale profile") that controls the asymptotic behavior of the solutions.

58 pages. This is the abridged and more reader-friendly version 2. Version 1 has full details

References in corpus (3)

• A pseudoconformal compactification of the nonlinear Schrödinger equation and applications
• Small data scattering for the nonlinear Schrödinger equation on product spaces
• Global well-posedness and scattering for the defocusing quintic NLS in three dimensions