Semi-classical limit of the massive Klein-Gordon-Maxwell system toward the relativistic Euler-Maxwell system via an adapted modulated energy method

2025/02/10 by Tony Salvi, Salvi, Tony
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2502.06622

openalex publication_date 2025/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We show that the momentum, the density, and the electromagnetic field associated with the massive KleinGordon-Maxwell equations converge in the semi-classical limit towards their respective equivalents associated with the relativistic Euler-Maxwell equations. The proof relies on a modulated stress-energy method and a compactness argument. We also give a proof of the well-posedness of the relativistic Euler-Maxwell equations and show how this system, and so the semi-classical limit of Klein-Gordon-Maxwell, is related to the relativistic massive Vlasov-Maxwell equations.

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