Pith Number

pith:ZBPSPEMD

pith:2026:ZBPSPEMDHFY4BUFRJNWFNX45ZD

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Stochastic Euler Equations with Pseudo-differential Noise: Continuous and Discontinuous Perturbations in Compressible and Incompressible Flows

Feng-Yu Wang, Hao Tang, Kenneth. H. Karlsen

Mixed continuous and discontinuous pseudo-differential noise yields local classical solutions to stochastic Euler equations and invariant measures for the damped incompressible case.

arxiv:2605.16963 v1 · 2026-05-16 · math.PR · math.AP

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Claims

C1strongest claim

This application gives what appears to be the first positive answer to Shirikyan's open problem on the damped Euler equations on T^2 under genuinely mixed multiplicative noise. Furthermore, our framework goes beyond the original formulation of the problem: it resolves a substantially strengthened version in every dimension d≥2, on both T^d and R^d.

C2weakest assumption

The pressure laws belong to a broad class (including piecewise Chaplygin-type laws and the white-dwarf equation of state) that permits a generalized Makino-type transformation while preserving the structure needed for classical solutions under the pseudo-differential noise.

C3one line summary

Develops local classical solution theory for stochastic Euler equations with pseudo-differential Stratonovich/Itô and Marcus noise and establishes a criterion for invariant probability measures that resolves Shirikyan's open problem in the damped incompressible case across dimensions.

References

101 extracted · 101 resolved · 0 Pith anchors

[1] Abels.Pseudodifferential and singular integral operators: An Introduction with Applications 2012

[2] S. Albeverio, Z. Brzeźniak, and A. Daletskii. Stochastic Camassa-Holm equation with convection type noise.J. Differential Equations, 276:404–432, 2021. 5 2021

[3] Alinhac.Blowup for nonlinear hyperbolic equations, volume 17 ofProgress in Nonlinear Differential Equa- tions and their Applications 1995

[4] D. Alonso-Orán and A. Bethencourt de León. On the well-posedness of stochastic Boussinesq equations with transport noise.J. Nonlinear Sci., 30(1):175–224, 2020. 5, 12 2020

[5] D. Alonso-Orán, C. Rohde, and H. Tang. A Local-in-Time Theory for Singular SDEs with Applications to Fluid Models with Transport Noise.J. Nonlinear Sci., 31(6):Paper No. 98, 2021. 5 2021

Receipt and verification

First computed	2026-05-20T00:03:33.214549Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c85f2791833971c0d0b14b6c56df9dc8e078dfd7cd25b5b90d664dac2d03a397

Aliases

arxiv: 2605.16963 · arxiv_version: 2605.16963v1 · doi: 10.48550/arxiv.2605.16963 · pith_short_12: ZBPSPEMDHFY4 · pith_short_16: ZBPSPEMDHFY4BUFR · pith_short_8: ZBPSPEMD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZBPSPEMDHFY4BUFRJNWFNX45ZD \
  | 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: c85f2791833971c0d0b14b6c56df9dc8e078dfd7cd25b5b90d664dac2d03a397

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f27841bc9f6f10bf55b55598d32c2f05b4cc4636db73824fe2571b1be2763a8a",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-16T12:36:43Z",
    "title_canon_sha256": "387b5b0a29539d5f6b65f1e5fa0ce65ba9602c413a2748bc0fe654ca38e494bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16963",
    "kind": "arxiv",
    "version": 1
  }
}