Global well-posedness and scattering for small data for the three-dimensional Kadomtsev-Petviashvili II equation

摘要

We study global well-posedness for the Kadomtsev-Petviashvili II equation in three space dimensions with small initial data. The crucial points are new bilinear estimates and the definition of the function spaces. As by-product we obtain that all solutions to small initial data scatter as t ->+/-infinity.