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

2011/08/04 by Sebastian Herr, Daniel Tataru, Nikolay Tzvetkov
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Nonlinear Partial Differential Equations

paper · doi:10.1215/00127094-1415889

Abstract

A refined trilinear Strichartz estimate for solutions to the Schrödinger equation on the flat rational torus T3 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 Hs(T3) for all s≥1. This is the first energy-critical global well-posedness result in the setting of compact manifolds.

Citations

• Bilinear eigenfunction estimates and the nonlinear Schr�dinger equation on surfaces

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