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Stabilization by transport noise and enhanced dissipation in the Kraichnan model

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arxiv 2104.03949 v3 pith:JKKTVAEL submitted 2021-04-08 math.PR math.APmath.DS

Benjamin Gess , Ivan Yaroslavtsev This is my paper · ORCID
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keywords transportstabilizationsufficientconditionsdissipationenhancedgivenkraichnan
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Stabilization and sufficient conditions for mixing by stochastic transport are shown. More precisely, given a second order linear operator with possibly unstable eigenvalues on a smooth compact Riemannian manifold, it is shown that the inclusion of transport noise can imply global asymptotic stability. Moreover, it is shown that an arbitrary large exponential rate of convergence can be reached, implying enhanced dissipation. The sufficient conditions are shown to be satisfied by the so-called Kraichnan model for stochastic transport of passive scalars in turbulent fluids. In addition, an example is given showing that it can be sufficient to force four modes in order to induce stabilization.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Effective Lagrangian regularity and the uniqueness threshold for random H\"older velocity fields

    math.PR 2026-08 accept novelty 8.0 of 10

    For random multiscale Hölder velocity fields with finite-range dependence, uniqueness of ODE and transport solutions holds almost surely above the sharp threshold alpha=1/2, with explicit counterexamples below.

  2. A Stochastic RAGE Theorem and Enhanced Dissipation for Transport Noise

    math.AP 2025-07 conditional novelty 8.0 of 10

    A necessary and sufficient condition for enhanced dissipation under transport noise is the absence of non-trivial finite-dimensional invariant subspaces, with sharp rates for stochastic shear flows.

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    math.AP 2025-05 conditional novelty 8.0 of 10

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