Pith Number

pith:I5SHNBS4

pith:2026:I5SHNBS4NDK2KXLZS5XGOOD2P2

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Lagrangian chaos for the 2D Navier-Stokes equations driven by mildly degenerate noise

Dengdi Chen, Yan Zheng

The 2D Navier-Stokes equations driven by mildly degenerate low-mode noise have a strictly positive top Lyapunov exponent in their Lagrangian flow.

arxiv:2603.26806 v2 · 2026-03-26 · math.DS

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Claims

C1strongest claim

We prove that the top Lyapunov exponent of the associated Lagrangian flow is strictly positive, thereby establishing Lagrangian chaos.

C2weakest assumption

The noise is mildly degenerate and acts only on finitely many low Fourier modes, allowing controllability in the low-frequency subsystem while high modes dissipate.

C3one line summary

The top Lyapunov exponent of the Lagrangian flow for 2D incompressible Navier-Stokes equations driven by mildly degenerate noise on low modes is strictly positive.

References

35 extracted · 35 resolved · 0 Pith anchors

[1] Dynamical systems approach to turbulence[M] 1998

[2] Lagrangian chaos and scalar advection in stochastic fluid mechanics[J] 2022

[3] Almost-sure exponential mixing of passive scalars by the stochastic Navier–Stokes equations[J] 2022

[4] Mathematics of two-dimensional turbulence[M] 2012

[5] Gibbsian Dynamics and Ergodicity for the Stochastically Forced Navier–Stokes Equation[J] 2001

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:15.645708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

476476865c68d5a55d79976e67387a7e90c883051873e39969c6528ed260a299

Aliases

arxiv: 2603.26806 · arxiv_version: 2603.26806v2 · doi: 10.48550/arxiv.2603.26806 · pith_short_12: I5SHNBS4NDK2 · pith_short_16: I5SHNBS4NDK2KXLZ · pith_short_8: I5SHNBS4

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/I5SHNBS4NDK2KXLZS5XGOOD2P2 \
  | 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: 476476865c68d5a55d79976e67387a7e90c883051873e39969c6528ed260a299

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "dce992e1ced410e9e0b0439485beda82e1e40b610c797698b7dcc3f9a62d3207",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-03-26T08:10:59Z",
    "title_canon_sha256": "a84783cbc09433869c8a7bf124578a59bcf31a019bcdc70d80ab983790f03a2d"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 2
  }
}