Corrigendum to "Optimal time-decay estimates for an Oldroyd-B model with zero viscosity [J. Differential Equations, 306(2022), 456--491]"

Huanyao Wen; Jinrui Huang; Ruizhao Zi; Yinghui Wang

arxiv: 2604.09636 · v1 · submitted 2026-03-20 · 🧮 math.AP

Corrigendum to "Optimal time-decay estimates for an Oldroyd-B model with zero viscosity [J. Differential Equations, 306(2022), 456--491]"

Jinrui Huang , Yinghui Wang , Huanyao Wen , Ruizhao Zi This is my paper

Pith reviewed 2026-05-15 08:36 UTC · model grok-4.3

classification 🧮 math.AP

keywords Oldroyd-B modeltime-decay estimateszero viscosityviscoelastic fluidcorrigendumpartial differential equations

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The pith

The assumption stated in Theorem 1.2 of the 2022 Oldroyd-B paper requires a minor correction to close a gap in the proof.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This note supplies a minor correction to the assumption of Theorem 1.2 and the corresponding steps in its proof from the authors' earlier 2022 paper on optimal time-decay estimates for an Oldroyd-B model with zero viscosity. The original formulation of the assumption was imprecise, which opened a gap in the argument. Once the assumption is adjusted and the proof is revised accordingly, the claimed decay rates for the fluid variables remain valid. A reader would care because these estimates describe how solutions to the viscoelastic system settle over time, and the correction ensures the theorem applies precisely to the intended class of initial data.

Core claim

The present note identifies an imprecise assumption in Theorem 1.2 of the 2022 paper and supplies the corrected version together with the adjusted proof steps, thereby restoring the validity of the optimal time-decay estimates for the Oldroyd-B system with zero viscosity.

What carries the argument

The revised assumption on the initial data for the Oldroyd-B fluid equations that closes the gap and permits the time-decay estimates.

Load-bearing premise

The original assumption written in Theorem 1.2 was imprecise and therefore created a gap that the correction must close.

What would settle it

An explicit initial datum satisfying the conditions of the 2022 paper for which the original assumption fails while the decay estimates are still asserted.

read the original abstract

The present note is to make minor correction on the assumption of Theorem 1.2 and its proof in our paper [arXiv:2111.02059, Jinrui Huang, Yinghui Wang, Huanyao Wen and Rizhao Zi, {\it J. Differential Equations}, 306(2022), 456--491].

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A narrow technical corrigendum that fixes one assumption in Theorem 1.2 of the 2022 Oldroyd-B decay paper and supplies the matching proof tweak, with no change to the stated decay rates.

read the letter

This note corrects a minor flaw in the assumption used for Theorem 1.2 in the authors' 2022 JDE paper on time-decay estimates for the Oldroyd-B system with zero viscosity. They replace the original condition with a revised one and give a short adjustment to the argument that follows from it. The main decay rates themselves stay the same, and nothing else in the paper is altered. That is the entire content. The correction is presented cleanly and without extra claims, which is the right way to handle this kind of slip. Anyone who has already cited or applied the original theorem now has a precise statement of the condition under which the estimates are valid. The note is short, references the earlier work directly, and does not try to expand the result. The only real limitation is that it contains no new estimates or broader analysis; it is strictly a repair. Because the fix is local and the original paper's main conclusions are untouched, the impact is confined to readers who need the exact hypothesis for that single theorem. For the rest of the field the change is invisible. A specialist working on decay estimates for viscoelastic fluids would still want to know the corrected version, but the document does not introduce fresh mathematics that would shift ongoing research. It is the sort of note that deserves a quick referee check to confirm the revised assumption is correctly stated and that the adjusted proof steps are free of gaps, even though the scope is narrow. I would send it to review rather than desk-reject it.

Referee Report

0 major / 1 minor

Summary. This short corrigendum note corrects an erroneous assumption in the statement of Theorem 1.2 from the authors' 2022 paper on optimal time-decay estimates for the Oldroyd-B model with zero viscosity. It replaces the assumption with a corrected version and supplies a brief corresponding adjustment to the proof, while leaving the main decay rates and all other results unchanged.

Significance. The note ensures the logical validity of Theorem 1.2 by fixing a local technical gap in its hypothesis. Because the correction is presented as minor, confined to that theorem, and does not alter the central decay estimates or introduce new claims, it strengthens the reliability of the original published results without expanding their scope.

minor comments (1)

The note would be clearer if it explicitly quoted both the original (incorrect) assumption and the revised assumption for Theorem 1.2 side-by-side, rather than referring readers solely to the 2022 paper.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our corrigendum and the recommendation to accept. The note is intended as a minor technical correction to the hypothesis and proof of Theorem 1.2 in the 2022 paper, leaving all decay rates and other results unchanged.

Circularity Check

0 steps flagged

Corrigendum contains no derivations and no circular steps

full rationale

This document is a brief corrigendum that only replaces one assumption in the statement of Theorem 1.2 from the authors' 2022 paper and supplies the corresponding short proof adjustment. No new estimates, decay rates, or predictions are derived; the note simply references the prior work to correct a technical gap. Because the present text introduces no equations, ansatzes, or load-bearing arguments of its own, no step reduces to a self-definition, fitted input, or self-citation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This short corrigendum introduces no new free parameters, axioms, or invented entities; it only corrects an existing assumption from the referenced 2022 paper.

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Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

Huang, Y .H

J.R. Huang, Y .H. Wang, H.Y . Wen, R.Z. Zi, Optimal time-decay estimates for an Oldroyd-B model with zero viscosity. J. Differential Equations, 306(2022), 456–491

work page 2022
[2]

Schonbek, T.P

M.E. Schonbek, T.P. Schonbek, E. S¨uli, Large-time behaviour of solutions to the magnetohydrody- namics equations. Math. Ann., 304(1996), no.4, 717–756. 4

work page 1996

[1] [1]

Huang, Y .H

J.R. Huang, Y .H. Wang, H.Y . Wen, R.Z. Zi, Optimal time-decay estimates for an Oldroyd-B model with zero viscosity. J. Differential Equations, 306(2022), 456–491

work page 2022

[2] [2]

Schonbek, T.P

M.E. Schonbek, T.P. Schonbek, E. S¨uli, Large-time behaviour of solutions to the magnetohydrody- namics equations. Math. Ann., 304(1996), no.4, 717–756. 4

work page 1996