Pith Number

pith:CFKXT2OL

pith:2026:CFKXT2OLQMNNOHVRH7V7U5Z2W5

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Sharp decay characterization for the incompressible Oldroyd-B model in critical $L^p$ spaces

Jiahong Wu, Lvqiao Liu, Mingwen Fei, Zhi Chen

An L2-type low-frequency condition on initial data is almost necessary and sufficient for optimal upper and lower bounds on temporal decay of solutions to the incompressible Oldroyd-B model without viscosity or damping in critical Besov spaces.

arxiv:2605.13598 v1 · 2026-05-13 · math.AP

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4 Citations open

5 Replications open

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Claims

C1strongest claim

an L^2-type condition on the low-frequencies part of the initial data (u_0, τ_0) is almost both necessary and sufficient for obtaining optimal upper and lower bounds on the temporal decay of solutions in critical Besov spaces

C2weakest assumption

The new decomposition of the stress tensor into incompressible and compressible parts together with the effective tensor successfully controls the loss of regularity in high-frequency velocity without introducing uncontrolled errors or extra assumptions on the data.

C3one line summary

References

40 extracted · 40 resolved · 0 Pith anchors

[1] H. Bahouri, J.-Y. Chemin, and R. Danchin.Fourier analysis and nonlinear partial differ- ential equations, volume 343 ofGrundlehren der mathematischen Wissenschaften [Fun- damental Principles of Mathem 2011

[2] J. W. Barrett and S. Boyaval. Existence and approximation of a (regularized) Oldroyd-B model.Math. Models Methods Appl. Sci., 21(9):1783–1837, 2011 2011

[3] L. Brandolese. Characterization of solutions to dissipative systems with sharp algebraic decay.SIAM J. Math. Anal., 48(3):1616–1633, 2016. 48 ZHI CHEN, MINGWEN FEI, L VQIAO LIU, AND JIAHONG WU 2016

[4] L. Brandolese, L.-Y. Shou, J. Xu, and P. Zhang. Sharp decay characterization for the compressible Navier-Stokes equations.Adv. Math., 456:Paper No. 109905, 60, 2024 2024

[5] M. G. Brereton. Dynamics of polymeric liquids.Physics Bulletin, 29(1):26, 1978 1978

Receipt and verification

First computed	2026-05-18T02:44:22.970300Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

115579e9cb831ad71eb13febfa773ab74da03657e5383a146c62ce329988ed38

Aliases

arxiv: 2605.13598 · arxiv_version: 2605.13598v1 · doi: 10.48550/arxiv.2605.13598 · pith_short_12: CFKXT2OLQMNN · pith_short_16: CFKXT2OLQMNNOHVR · pith_short_8: CFKXT2OL

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CFKXT2OLQMNNOHVRH7V7U5Z2W5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 115579e9cb831ad71eb13febfa773ab74da03657e5383a146c62ce329988ed38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47a9230ecfe260a50383e81f0870fb08cf85049b0faa10f87333b91cc4c3220c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T14:33:17Z",
    "title_canon_sha256": "6b820151c89864798dd7342fd28aa9e94718afb3015bb007686f2ef525e51eec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13598",
    "kind": "arxiv",
    "version": 1
  }
}