Global Well-posedness of the Energy-Critical Defocusing NLS on Rectangular Tori in three Dimensions

Abstract

The energy-critical defocusing nonlinear Schrödinger equation on 3-dimensional rectangular tori is considered. We prove that the global well-posedness result for the standard torus of Ionescu and Pausader extends to this class of manifolds, namely, for any initial data in $H^1$ the solution exists globally in time.

15 pages

Cited by in corpus (2)

• On the global well-posedness for the periodic quintic nonlinear Schrödinger equation
• Growth of higher Sobolev norms for energy critical NLS on irrational tori: small energy case