Pith Number

pith:6NCC7HB3

pith:2026:6NCC7HB32NPK2GYP2OW3WU4T6R

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Global Yudovich-type solutions to a reduced model for micropolar fluids with zero viscosity

Francesco Fanelli, Pedro Gabriel Fern\'andez Dalgo

The 2D reduced micropolar fluid model admits global unique Yudovich solutions with only bounded vorticity.

arxiv:2605.13478 v1 · 2026-05-13 · math.AP

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Claims

C1strongest claim

For this model, we prove global existence and uniqueness of Yudovich-type solutions, namely weak solutions for which the vorticity is only bounded (with some additional integrability property) and the microrotation field remains bounded and of finite energy.

C2weakest assumption

The reduced 2D system obtained from micropolar fluid dynamics with zero viscosity preserves the transport and boundedness properties needed for the Yudovich estimates to close under the given coupling.

C3one line summary

Global existence and uniqueness of bounded-vorticity weak solutions is established for a 2D micropolar fluid model with zero viscosity.

References

26 extracted · 26 resolved · 0 Pith anchors

[1] Instability and non-uniqueness for the 2D Euler equations, after M. Vishik 2024

[2] Fourier analysis and nonlinear partial differential equa- tions 2011

[3] A. Béjar-López, C. Cunha, J. Soler:Two-dimensional incompressible micropolar fluid models with singular initial data. Phys. D.,430(2022), Paper No. 133069 2022

[4] Chemin:Sur le mouvement des particules d’un fluide parfait incompressible bidimensionel 1991

[5] Chemin:Persistance des structures géométriques liées aux poches de tourbillon 1993

Receipt and verification

First computed	2026-05-18T02:44:41.412130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3442f9c3bd35ead1b0fd3adbb5393f4525348b9f79c0752b7b33c794a725355

Aliases

arxiv: 2605.13478 · arxiv_version: 2605.13478v1 · doi: 10.48550/arxiv.2605.13478 · pith_short_12: 6NCC7HB32NPK · pith_short_16: 6NCC7HB32NPK2GYP · pith_short_8: 6NCC7HB3

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6NCC7HB32NPK2GYP2OW3WU4T6R \
  | 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: f3442f9c3bd35ead1b0fd3adbb5393f4525348b9f79c0752b7b33c794a725355

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48dbd408de4e5808609aa91baabd8ee485f808202024455084e7c635270bc9e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T13:03:28Z",
    "title_canon_sha256": "00083f9d8c6ef19c8c0e5bd93f4b337ed4d36130bb7f904b4782f6a60c5c9b6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13478",
    "kind": "arxiv",
    "version": 1
  }
}