论文标题
传输理论中的定量流体近似：一种统一的方法
Quantitative fluid approximation in transport theory: a unified approach
论文作者
论文摘要
我们为整个空间中的\ emph {Linear}碰撞动力学方程的大时空缩放极限提出了一种统一方法。极限是\ emph {分数}的扩散类型，用于重尾平衡，较慢，而扩散类型则否则。证明是建设性的，并且获得了分数/标准扩散矩阵。该方法结合了能量估计和定量光谱方法来构建“流体模式”。该方法应用于散射模型（不假设详细的平衡条件），Fokker-Planck运营商和L {é} Vy-Fokker-Planck运营商。它证明了一系列新结果，包括在任何维度上对Fokker-Planck运营商的分数扩散极限，为此，扩散系数的公式尚不清楚，因为L {é} vy-fokker-Planck操作员与一般平衡器具有一般性的均衡器，以及用于散射某些Infinite squeporibribria的散射。它还以定量方法统一并概括了先前论文的结果，而我们对流体近似误差的估计似乎也很新。
We propose a unified method for the large space-time scaling limit of \emph{linear} collisional kinetic equations in the whole space. The limit is of \emph{fractional} diffusion type for heavy tail equilibria with slow enough decay, and of diffusive type otherwise. The proof is constructive and the fractional/standard diffusion matrix is obtained. The method combines energy estimates and quantitative spectral methods to construct a `fluid mode'. The method is applied to scattering models (without assuming detailed balance conditions), Fokker-Planck operators and L{é}vy-Fokker-Planck operators. It proves a series of new results, including the fractional diffusive limit for Fokker-Planck operators in any dimension, for which the formulas for the diffusion coefficient were not known, for L{é}vy-Fokker-Planck operators with general equilibria, and for scattering operators including some cases of infinite mass equilibria. It also unifies and generalises the results of previous papers with a quantitative method, and our estimates on the fluid approximation error also seem novel.
