Global Strichartz estimates for the Dirac equation on symmetric spaces

TL;DR

This paper establishes global-in-time weighted Strichartz estimates for the Dirac equation on warped product spaces, including eigenspace restrictions and estimates with angular derivative loss, advancing understanding of Dirac dynamics on symmetric manifolds.

Contribution

It provides new global Strichartz estimates for the Dirac equation on warped product spaces, including eigenspace restrictions and estimates with angular derivative loss, under explicit metric conditions.

Findings

Establishes global weighted Strichartz estimates for the Dirac equation on symmetric spaces.

Derives estimates restricted to eigenspaces of the Dirac operator.

Provides estimates with angular derivative loss for general initial data.

Abstract

In this paper we study global-in-time, weighted Strichartz estimates for the Dirac equation on warped product spaces in dimension $n\geq3$. In particular, we prove estimates for the dynamics restricted to eigenspaces of the Dirac operator on the compact spin manifolds defining the ambient manifold under some explicit sufficient condition on the metric, and estimates with loss of angular derivatives for general initial data in the setting of spherically symmetric and asymptotically flat manifolds.