Strichartz estimates for the Dirac equation on asymptotically flat manifolds

TL;DR

This paper establishes Strichartz estimates for the Dirac equation on asymptotically flat manifolds by combining dispersive and smoothing estimates from related wave equations, advancing understanding of dispersive PDEs in curved geometries.

Contribution

It introduces new Strichartz estimates for the Dirac equation on asymptotically flat manifolds, integrating recent dispersive results in this geometric setting.

Findings

Proved Strichartz estimates for the Dirac equation in asymptotically flat manifolds.

Combined dispersive estimates with wave and Klein-Gordon estimates.

Extended the analysis of dispersive PDEs to curved geometrical backgrounds.

Abstract

In this paper we prove Strichartz estimates for the Dirac equation on asymptotically flat manifolds. The proof combines the weak dispersive estimates proved by the first two authors with the Strichartz and smoothing estimates for the wave and Klein-Gordon flows, exploiting some recent results in the same geometrical setting.