从二维流体动力学中的加性噪声到输运噪声
From additive to transport noise in 2D fluid dynamics
摘要：
偏微分方程中的加性噪声，特别是流体力学中的加性噪声，具有相对自然的动机。这项工作的目的是表明，适当的多尺度参数导致严格的，从流体模型添加剂噪声，运输型噪声。这些论点既适用于作用于大尺度被动标量的流体的小尺度随机扰动，也适用于前者对流体本身的大尺度的作用。我们的方法包括在研究的（随机）特性相关的小规模随机扰动的流体，这里建模随机二维欧拉方程加性噪声，和他们的收敛在无限大规模的分离限制。
英文摘要：
Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with additive noise, to transport type noise. The arguments apply both to small-scale random perturbations of the fluid acting on a large-scale passive scalar and to the action of the former on the large scales of the fluid itself. Our approach consists in studying the (stochastic) characteristics associated to small-scale random perturbations of the fluid, here modelled by stochastic 2D Euler equations with additive noise, and their convergence in the infinite scale separation limit.
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