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Turbulent diffusion in Markovian flows. (English) Zbl 0960.60034

The authors present turbulent diffusion theorems for Markovian velocity fields which either are mixing in time or have stationary vector potentials. The authors prove an invariance principle for deterministic motion as well as diffusive motion in a general class of time-mixing, Markovian velocity fields with no decorrelation in space. Moreover, the authors show that small molecular diffusion acts as a regular perturbation to a positive eddy diffusity.

MSC:

60F17 Functional limit theorems; invariance principles
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
60G44 Martingales with continuous parameter
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