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<p>We show that the momentum, the density, and the electromagnetic field associated with the massive Klein–Gordon–Maxwell equations converge in the semiclassical limit toward their respective equivalents associated with the relativistic pressureless 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 pressureless Euler–Maxwell equations and show how this system, and so the semiclassical limit of Klein–Gordon–Maxwell, is related to the relativistic massive Vlasov–Maxwell equations.</p>

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Semi-classical Limit of the Massive Klein–Gordon–Maxwell System Toward the Relativistic Pressureless Euler–Maxwell System via an Adapted Modulated Energy Method

  • 期刊论文

  • 发表日期：

    2025年11月8日

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  • Tony Salvi

摘要

We show that the momentum, the density, and the electromagnetic field associated with the massive Klein–Gordon–Maxwell equations converge in the semiclassical limit toward their respective equivalents associated with the relativistic pressureless 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 pressureless Euler–Maxwell equations and show how this system, and so the semiclassical limit of Klein–Gordon–Maxwell, is related to the relativistic massive Vlasov–Maxwell equations.