Poincare-Dulac Normal Form Reduction for Unconditional Well-Posedness of the Periodic Cubic NLS

Abstract

We implement an infinite iteration scheme of Poincar,-Dulac normal form reductions to establish an energy estimate on the one-dimensional cubic nonlinear Schrodinger equation (NLS) in , without using any auxiliary function space. This allows us to construct weak solutions of NLS in with initial data in as limits of classical solutions. As a consequence of our construction, we also prove unconditional well-posedness of NLS in for s >= 1/6.