Global well-posedness and scattering for small data for the 3-d KP-II Cauchy problem

TL;DR

This paper proves that for small initial data, the 3D KP-II equation is globally well-posed and solutions scatter, using new bilinear estimates and specialized function spaces.

Contribution

It introduces new bilinear estimates and function spaces to establish global well-posedness and scattering for the 3D KP-II equation with small initial data.

Findings

Global well-posedness for small data established

Solutions to the equation scatter over time

New bilinear estimates are developed

Abstract

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.