AI 中文总结
本文通过改编重整化能量方法，证明了相对论牛顿动力学的单动力学平均场极限，得到相对论Euler-Poisson方程，并首次建立了相对论Coulomb流的平均场极限。
AI 中文摘要
我们改编了\cite{duerinckx2020mean}中发展的重整化能量方法，以证明相对论牛顿动力学的单动力学平均场极限。由此得到的单动力学偏微分方程是相对论Euler-Poisson方程。由于位置相对于动量以相对论方式演化，调制能量的动力学部分必须进行调整，这导致了非相对论情形中不存在的进一步障碍。我们研究了相对论Euler-Poisson方程的弱-强稳定性原理，随后通过重整化程序得到平均场极限。我们的主要结果构成了相对论Coulomb流的第一个平均场极限。
英文摘要
We adapt the renormalized energy method developed in \cite{duerinckx2020mean} in order to prove the monokinetic mean field limit for relativistic Newtonian dynamics. The resulting monokinetic PDE is the relativistic Euler-Poisson equation. Since the position evolves relativistically in comparison to the momentum, the kinetic part of the modulated energy has to adjusted, leading to further obstructions that are not present in the non-relativistic settings. A weak-strong stability principle for the relativistic Euler-Poisson equation is investigated, followed by a renormalization procedure leading to the mean-field limit. Our main result constitute the first mean-field limit for relativistic Coulomb flows.
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