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Deterministic 3D-Perturbations of Planar Incompressible Flow Lead to Stochasticity

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Abstract

We show that the long-time behavior of the stationary incompressible flow in R 3, which is close to a planar one, under broad generic assumptions, is, in a sense, stochastic. This stochasticity is a result of instability of the corresponding planar flow near the saddle points of the stream function. The stochastic process which describes long-time evolution of the slow component of the motion is calculated.

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Authors and Affiliations

  1. University of Maryland, College Park

    Mark Freidlin

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  1. Mark Freidlin
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Freidlin, M. Deterministic 3D-Perturbations of Planar Incompressible Flow Lead to Stochasticity. Journal of Statistical Physics 111, 1209–1218 (2003). https://doi.org/10.1023/A:1023052216159

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  • DOI: https://doi.org/10.1023/A:1023052216159

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