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Low regularity well-posedness of the Dirac-Klein-Gordon equations in one space dimension

2006/11/23 by Sigmund Selberg, Selberg, Sigmund, Achenef Tesfahun +1
Engineering · Mathematics · #35L70 #35Q40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0611718

openalex publication_date 2006/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend recent results of S. Machihara and H. Pecher on low regularity well-posedness of the Dirac-Klein-Gordon (DKG) system in one dimension. Our proof, like that of Pecher, relies on the null structure of DKG, recently completed by D'Ancona, Foschi and Selberg, but we show that in 1d the argument can be simplified by modifying the choice of projections for the Dirac operator. We also show that the result is best possible up to endpoint cases, if one iterates in Bourgain-Klainerman-Machedon spaces.

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