Low Regularity local well-posedness for the 1+3 dimensional Dirac-Klein-Gordon system

TL;DR

This paper establishes local well-posedness for the 1+3 dimensional Dirac-Klein-Gordon system in low regularity Sobolev spaces, extending previous results by leveraging null structure and bilinear estimates.

Contribution

It introduces new well-posedness results for the Dirac-Klein-Gordon system in lower regularity spaces using advanced analytical techniques.

Findings

Proves local well-posedness in broader Sobolev spaces.

Utilizes null structure and bilinear spacetime estimates.

Extends previous well-posedness results.

Abstract

We prove that the Cauchy problem for the Dirac-Klein-Gordon system of equations in 1+3 dimensions is locally well-posed in a range of Sobolev spaces for the Dirac spinor and the meson field. The result contains and extends the earlier known results for the same problem. Our proof relies on the null structure in the system, and bilinear spacetime estimates of Klainerman-Machedon type.