Pith. sign in

REVIEW 2 cited by

A Unified Approach to Mixing and Regularity for Passive Scalar Transport by Sobolev Vector Fields

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 2402.11642 v3 pith:VU6UQMVR submitted 2024-02-18 math.AP

Lucas Huysmans , Ayman Rimah Said This is my paper
classification math.AP
keywords approachdiperna-lionsestimatesfieldslogarithmicmixingpassivequantitative
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We develop a new framework for quantitative estimates of passive scalar transport along Sobolev vector fields in $W^{1,p}$, when $p>1$. Our approach is based on Christ-Journ\'{e} singular integral estimates. We show (i) a new stability estimate which quantifies the dependence of the solution on specific frequencies of the initial data; (ii) a new exponential mixing bound in the full DiPerna-Lions well-posedness class; (iii) propagation of logarithmic Fourier regularity of the solution; (iv) quantitative convergence rates for the vanishing diffusivity and mollification limits; and (v) a logarithmic decay rate for the standard DiPerna-Lions commutator.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Osgood meets Ambrosio-DiPerna-Lions

    math.AP 2026-07 accept novelty 6.0 of 10

    Bounded distributional solutions of the transport equation are unique and renormalized under an L^p Osgood condition on a divergence-free vector field.

  2. Regularity estimates in transport equations via heat flow and quantitative differentiation

    math.AP 2026-07 conditional novelty 6.0 of 10

    Quantitative estimates for the Ambrosio–Trevisan and DiPerna–Lions commutators are proved via heat flow and quantitative differentiation, yielding log-Sobolev regularity propagation for transport equations.

Pith tools