Unconditional local well-posedness for periodic NLS

Abstract

Nonlinear Schrödinger equations with nonlinearities |u|2ku on the d-dimensional torus are considered for arbitrary positive integers k and d. The solution of the Cauchy problem is shown to be unique in the class CtHxs for a certain range of scale-subcritical regularities s, which is almost optimal in the case d≥4 or k≥2. The proof is based on various multilinear estimates and the infinite normal form reduction argument.