Many nonlinear dispersive partial differential equations exhibit a phenomenon where the nonlinear part of the evolution, in the Duhamel integral formula, is slightly more regular than the purely linear evolution, for the same initial data. This is usually called nonlinear smoothing and is also intimately connected to dispersive blow up. We show how the infinite normal form reduction method, developed in the past few years to prove unconditional uniqueness of initial value problems, can be applied to provide a broad and general approach for establishing nonlinear smoothing of several different dispersive PDEs.

This is joint work with Simão Correia.