Multilinear oscillatory integrals and estimates for coupled systems of dispersive PDEs

Aksel Bergfeldt, Salvador Rodriguez-Lopez, David Rule, Wolfgang Staubach

Published 2023-01-31Version 1

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.