Multilinear oscillatory integrals and estimates for coupled systems of dispersive PDEs

TL;DR

This paper proves sharp regularity results for multilinear oscillatory integrals linked to nonlinear dispersive PDEs and demonstrates local continuous dependence on initial data for coupled dispersive systems.

Contribution

It introduces new regularity estimates for multilinear oscillatory integrals and establishes local well-posedness results for coupled dispersive PDE systems.

Findings

Sharp global regularity of multilinear oscillatory integrals.

Continuous dependence on initial data for coupled dispersive PDEs.

Applicability to systems with Banach and quasi-Banach target spaces.

Abstract

We establish sharp global regularity of a class of multilinear oscillatory integral operators that are associated to nonlinear dispersive equations with both Banach and quasi-Banach target spaces. As a consequence we also prove the (local in time) continuous dependence on the initial data for solutions of a large class of coupled systems of dispersive partial differential equations.