Strichartz Estimates for a Class of Baouendi-Grushin Operators

TL;DR

This paper establishes Strichartz estimates for a class of Baouendi--Grushin operators on Euclidean spaces and manifolds, and applies these results to analyze the Schrödinger equations associated with these operators.

Contribution

It introduces new Strichartz estimates for Baouendi--Grushin operators on Euclidean spaces and product manifolds, and demonstrates their application to Schrödinger equation analysis.

Findings

Proved Strichartz estimates for Baouendi--Grushin operators.

Applied estimates to the Cauchy problem for Schrödinger equations.

Extended results to operators on product spaces with compact manifolds.

Abstract

We prove Strichartz estimates for a class of Baouendi--Grushin operators acting either on the Euclidean space or a product of the type $\mathbb{R}^{d_1} \times M$, where $(M,g)$ is a smooth compact manifold with no boundary. We then give an application of these Strichartz estimates to the Cauchy theory for the associated Schr\"odinger equations.