Global well-posedness of the energy critical Nonlinear Schrödinger equation with small initial data in H^1(T^3)

Abstract

A refined trilinear Strichartz estimate for solutions to the Schrödinger 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 Schrödinger 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.

v3: 19 pages

References in corpus (1)

• Well-posedness and scattering for the KP-II equation in a critical space

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