We deal with the problem of separation of time-scales and filamentation in a linear drift-diffusion problem posed on the whole space ${\mathbb{R}}^2$. The passive scalar considered is stirred by an incompressible flow with radial symmetry. We identify a time-scale, much faster than the diffusive one, at which mixing happens along the streamlines, as a result of the interaction between transport and diffusion. This effect is also known as enhanced dissipation. The proofs are based on an adaptation of a hypocoercivity scheme and yield a linear semigroup estimate in a suitable weighted $L^2$-based space.

中文翻译：

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时滞扩散方程的时间尺度分离。 ${\mathbb{[R}}^2$

我们处理在整个空间上构成的线性漂移扩散问题中的时间标度和细丝分离问题 ${\mathbb{[R}}^2$。所考虑的被动标量由具有径向对称性的不可压缩流搅动。我们确定了一个时标，比扩散时要快得多，在该时标中，由于运输和扩散之间的相互作用，沿着流线发生了混合。这种效应也称为增强的耗散。证明基于低矫顽力方案的改编，并在适当的加权下得出线性半群估计${\mathrm{大号}}^2$空间。