论文标题
随机匀浆，无时无差异
Stochastic homogenization with space-time ergodic divergence-free drift
论文作者
论文摘要
我们证明，具有时空固定和厄贡，无差异的漂移在法律上均质的扩散方程与Stratonovich传输噪声的确定性随机部分微分方程。在没有空间的终身制的情况下，通过使用适当定义的流矩阵，漂移仅部分吸收到通量的偏斜部分中。这留下了时间依赖性的，空间源的运输，对于轻度去相关的磁场，在同质化极限中以确定性的协方差收敛到布朗噪声。结果适用于均匀的椭圆形，固定和恒星环境，在该环境中，漂移允许适当定义的固定式和$ l^2 $ - 积分流矩阵。
We prove that diffusion equations with a space-time stationary and ergodic, divergence-free drift homogenize in law to a deterministic stochastic partial differential equation with Stratonovich transport noise. In the absence of spatial ergodicity, the drift is only partially absorbed into the skew-symmetric part of the flux through the use of an appropriately defined stream matrix. This leaves a time-dependent, spatially-homogenous transport which, for mildly decorrelating fields, converges to a Brownian noise with deterministic covariance in the homogenization limit. The results apply to uniformly elliptic, stationary and ergodic environments in which the drift admits a suitably defined stationary and $L^2$-integrable stream matrix.
