Low regularity local well-posedness for the Maxwell-Klein-Gordon\n equations in Lorenz gauge

2013/08/07 by Hartmut Pecher, Pecher, Hartmut · 1 citation
Engineering · Mathematics · Medicine · Physics and Astronomy · #35L70 #35Q61 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Soft tissue tumor case studies #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1308.1598

openalex publication_date 2013/08/07 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

The Cauchy problem for the Maxwell-Klein-Gordon equations in Lorenz gauge in\ntwo and three space dimensions is locally well-posed for low regularity data\nwithout finite energy. The result relies on the null structure for the main\nbilinear terms which was shown to be not only present in Coulomb gauge but also\nin Lorenz gauge by Selberg and Tesfahun, who proved global well-posedness for\nfinite energy data in three space dimensions. This null structure is combined\nwith product estimates for wave-Sobolev spaces given systematically by\nd'Ancona, Foschi and Selberg.\n

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