Almost optimal local well-posedness of the Maxwell-Klein-Gordon equations in 1+4 dimensions

2001/01/13 by Sigmund Selberg, Selberg, Sigmund
Engineering · Mathematics · #35L70 #35Q40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35L70 #msc:35Q40

paper · pdf · doi:10.48550/arxiv.math/0101120

openalex publication_date 2001/01/13 · arxiv created 2002/02/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Maxwell-Klein-Gordon equations on \R¹⁺⁴ relative to the Coulomb gauge are locally well-posed for initial data in H^1+ε for all ε> 0. This builds on previous work by Klainerman and Machedon who proved the corresponding result for a model problem derived from the Maxwell-Klein-Gordon system by ignoring the elliptic features of the system, as well as cubic terms.

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