Strichartz estimates for Baouendi–Grushin operators

Abstract

We prove Strichartz estimates for a class of Baouendi–Grushin operators acting either on the Euclidean space or on 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 Schrödinger equations.