Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ${\mathbb{R}}^2$ $\times$ ${\mathbb{T}}^2$

Abstract

We consider the problem of large data scattering for the defocusing cubic nonlinear Schrödinger equation on ${\mathbb{R}}^2$ $\times$ ${\mathbb{T}}^2$. This equation is critical both at the level of energy and mass. The key ingredients contain a global-in-time Stricharz estimate, resonant system approximation and profile decomposition. Assuming the large data scattering for the 2d cubic resonant system, we can prove the large data scattering for this problem.

40 pages. The author used a compact template which may be better with no big changes. It will appear in Journal of Hyperbolic Differential Equations. arXiv admin note: substantial text overlap with arXiv:1205.6132, arXiv:1101.4527 by other authors

References in corpus (4)

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• Global well-posedness and scattering for nonlinear Schrödinger equations with combined nonlinearities in the radial case
• Small data scattering for the nonlinear Schrödinger equation on product spaces
• The defocusing quintic NLS in four space dimensions

Cited by in corpus (2)

• Global Well-Posedness of the Energy-Critical Nonlinear Schrödinger Equation on ${\mathbb{T}}^4$
• On scattering for the defocusing nonlinear Schrödinger equation on waveguide ${\mathbb{R}}^m$ $\times$ $\mathbb{T}$ (when $m=2,3$)