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 Schr\"odinger equation on the flat rational torus 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 Schr\"odinger Equation in H^s(T^3) for all s \geq 1. This is the first energy-critical global well-posedness result in the setting of compact manifolds.