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

2007/06/25 by Achenef Tesfahun, Tesfahun, Achenef
Engineering · Mathematics · Physics and Astronomy · #35L70 #35Q40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.0706.3618

openalex publication_date 2007/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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