Dispersive estimates and NLS on product manifolds

TL;DR

This paper establishes dispersive estimates for Schrödinger equations on product manifolds, enabling analysis of multi-particle quantum systems and nonlinear equations on hyperbolic spaces.

Contribution

It provides a general framework for dispersive estimates on product manifolds, extending previous results to new geometric settings and applications.

Findings

Dispersive estimates are proven for Schrödinger equations on product manifolds.

Applications include two-particle Schrödinger equations on Euclidean spaces.

Results extend to nonlinear Schrödinger equations on hyperbolic spaces.

Abstract

We prove a general dispersive estimate for a Schroedinger type equation on a product manifold, under the assumption that the equation restricted to each factor satisfies suitable dispersive estimates. Among the applications are the two-particle Schroedinger equations on Euclidean spaces, and the nonlinear Schroedinger equation on the product of two real hyperbolic spaces.