Pith. sign in

REVIEW 5 cited by

Anomalous dissipation and Euler flows

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2310.02934 v2 pith:2NQODK7N submitted 2023-10-04 math.AP

Jan Burczak , László Székelyhidi Jr. , Bian Wu This is my paper
classification math.AP
keywords scalaradvectedanomalousdissipationeulerturbulencearbitrarybound
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We show anomalous dissipation of scalars advected by weak solutions to the incompressible Euler equations with $C^{(\sfrac{1}{3})^-}$ regularity, for an arbitrary initial datum in $\dot H^1 (\T^3)$. This is the first rigorous derivation of zeroth law of scalar turbulence, where the scalar is advected by solution to an equation of hydrodynamics (unforced and deterministic). As a byproduct of our method, we provide a typicality statement for the drift, and recover certain desired properties of turbulence, including a lower bound on scalar variance commensurate with the Richardson pair dispersion hypothesis.

Discussion (0). Sign in to comment.

Forward citations

Cited by 5 Pith papers

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

  1. Optimal convergence rates in multiscale elliptic homogenization

    math.AP 2025-09 conditional novelty 8.0 of 10

    For real analytic, multiply periodic coefficients, multiscale elliptic homogenization converges at rate epsilon1 + max_i e^{-c epsilon_i/epsilon_{i+1}}, and the exponential part is shown optimal up to the constant c.

  2. Superexponential dissipation enhancement on $\mathbb{T}^d$

    math.AP 2025-09 conditional novelty 8.0 of 10

    For advection-diffusion on T^d there exist incompressible velocity fields and initial data whose L2 mass decays double exponentially in 2D, like e^{-Ct^2} in 3D, and superexponentially in 4D.

  3. Exponentially mixing flows with slow enhanced dissipation

    math.PR 2025-07 conditional novelty 8.0 of 10

    Random alternating shear flows on the torus mix exponentially with diffusivity-independent rates yet have dissipation time of order 1/κ, showing enhanced dissipation is not implied by exponential mixing for merely C0 flows.

  4. Non-selection of Lagrangian trajectories in the zero-noise limit for a class of stochastic regularizations

    math.PR 2026-06 unverdicted novelty 7.0 of 10

    Proves lack of selection of Lagrangian trajectories in the zero-noise limit for SDEs with divergence-free Hölder-α vector fields (α close to 1) under broad additive noises, via Lagrangian flows and stochastic sewing l...

  5. 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.

Pith tools