标题： 一种随机RAGE定理和输运噪声的增强耗散 显示英文标题

标题： A Stochastic RAGE Theorem and Enhanced Dissipation for Transport Noise

摘要： 我们证明了一个随机版本的经典RAGE定理，适用于由噪声传输方程生成的两点运动。 作为结果，我们确定了相应的扩散方程为耗散增强的充要条件。 这涉及识别一个非平凡的、有限维的子空间，该子空间对于表征传输噪声结构的一族自伴算子是不变的。 我们讨论了几个例子，并证明了随机剪切流的尖锐增强耗散率。 显示英文摘要

摘要： We prove a stochastic version of the classical RAGE theorem that applies to the two-point motion generated by noisy transport equations. As a consequence, we identify a necessary and sufficient condition for the corresponding diffusive equation to be dissipation enhancing. This involves the identification of a non-trivial, finite dimensional subspace that is invariant for the family of self-adjoint operator characterizing the structure of the transport noise. We discuss several examples and prove a sharp enhanced dissipation rate for stochastic shear flows.