论文标题
从显微镜到宏观尺度方程：平均场，流体动力和图限
From microscopic to macroscopic scale equations: mean field, hydrodynamic and graph limits
论文作者
论文摘要
考虑到有限的粒子系统，我们详细阐述了各种方法，以将其传递到极限，因为代理的含量倾向于无穷大，要么通过平均场极限，得出vlasov方程，还是通过流体动力或图形极限，获得Euler方程。我们提供收敛量。我们还展示了如何通过摄取足够的ememotements从liouville到弗拉索夫或欧拉。我们的结果包括文献的许多已知结果并概括了我们的分析的令人惊讶的结果，我们表明，任何线性PDE的足够规则的溶液可以通过N颗粒系统的解决方案近似于1/ log log log（n）。
Considering finite particle systems, we elaborate on various ways to pass to the limit as thenumber of agents tends to infinity, either by mean field limit, deriving the Vlasov equation,or by hydrodynamic or graph limit, obtaining the Euler equation. We provide convergenceestimates. We also show how to pass from Liouville to Vlasov or to Euler by taking adequatemoments. Our results encompass and generalize a number of known results of the literature.As a surprising consequence of our analysis, we show that sufficiently regular solutions of anylinear PDE can be approximated by solutions of systems of N particles, to within 1/ log log(N ).
