Sharp ill-posedness of the Dirac-Klein-Gordon system in one dimension

TL;DR

This paper demonstrates the ill-posedness of the Dirac-Klein-Gordon system in one dimension at critical Sobolev regularities, completing the classification of well-posedness and ill-posedness in this context.

Contribution

It establishes the ill-posedness in the critical Sobolev space and completes the classification of regularities for well-posedness of the system.

Findings

Ill-posedness in critical Sobolev space

Classification of regularities for well-posedness

Completes the understanding of the system's behavior

Abstract

We show the ill-posedness of the Cauchy problem for the Dirac-Klein-Gordon system in one dimension in the critical Sobolev space. From this, we finish the classification of the regularities for which this problem is well-posed or ill-posed.