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Anomalous Regularization in Kraichnan's Passive Scalar Model

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arxiv 2407.16668 v2 pith:ELSRXNT4 submitted 2024-07-23 math.PR math.AP

Lucio Galeati , Francesco Grotto , Mario Maurelli This is my paper
classification math.PRmath.AP
keywords modelpassivescalaranomalouskraichnanregularizationsobolevadvection
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We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and H\"older regular in space (rough Kraichnan's model), a well established synthetic model of passive scalar turbulence. By studying the evolution of negative Sobolev norms, we show an anomalous regularization effect induced by the dynamics: distributional initial conditions immediately become functions of positive Sobolev regularity.

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Cited by 4 Pith papers

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

  1. Regularity thresholds for anomalous dissipation and related phenomena in passive scalars

    math.AP 2026-03 conditional novelty 8.0 of 10

    Random divergence-free velocity fields satisfying a zero-set (d=2) or derivative small-ball (d≥3) condition almost surely enforce the DiPerna-Lions property, preventing anomalous dissipation and related turbulent laws...

  2. Zero-noise selection and Large Deviations in $L^\infty_t L^p_x$ for the stochastic transport equation beyond DiPerna-Lions

    math.PR 2025-06 conditional novelty 8.0 of 10

    Rough transport noise selects the unique DiPerna-Lions solution in the zero-noise limit and yields a large deviations principle in the non-separable space L^∞_t L^p_x.

  3. A subsequentially fast dynamo on $\mathbb{T}^3$

    math.AP 2025-05 conditional novelty 8.0 of 10

    A smooth flow on T^3 is built so that the induction equation grows magnetic energy exponentially at rate at least 1/4, for any prescribed countable set of diffusivities accumulating at zero.

  4. Turbulent and intermittent phenomena in a universal total anomalous dissipator

    math.AP 2025-07 unverdicted novelty 6.0 of 10

    An explicit incompressible flow on the 2-torus is constructed that simultaneously causes anomalous dissipation, Richardson dispersion, anomalous regularization, and spatial intermittency for every Hölder exponent below 1.

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