Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in $H^1(\mathbb{T}^3)$

By Sebastian Herr, D. Tataru, Nikolay Tzvetkov. 2010

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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.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fe70a020e37e99793940007759cc68c68d76a01e