Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in H1(T3)

Abstract

A refined trilinear Strichartz estimate for solutions to the Schrödinger equation on the flat rational torus ${\mathbb{T}}^3$ is derived. By a suitable modification of critical function space theory this is applied to prove a small data global well-posedness result for the quintic nonlinear Schrödinger equation in $H^s({\mathbb{T}}^3)$ for all $s\ge 1$. This is the first energy-critical global well-posedness result in the setting of compact manifolds.