Pith Number

pith:3LVUUNEG

pith:2026:3LVUUNEGKPFPXJR2LMGLVJDCOF

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Leray--Hopf Type Weak Solutions for the Three-Dimensional Beris--Edwards System with Stable Landau--de Gennes Potential

Han Ni Soe, Yao Zhang, Zhipeng Xu

The Beris-Edwards system admits Leray-Hopf type weak solutions in three dimensions when the bulk potential is stable.

arxiv:2605.16997 v1 · 2026-05-16 · math.AP

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Claims

C1strongest claim

We prove existence of a weak solution to the three-dimensional Beris--Edwards system in the whole space under the stable bulk assumption c>0. The solution satisfies the natural bounds Q∈L^∞_t H^1_x ∩ L^2_t H^2_x and u∈L^∞_t L^2_x ∩ L^2_t H^1_x, the distributional form of the equations, and the expanded Leray--Hopf type energy inequality.

C2weakest assumption

The stable bulk assumption c>0 on the Landau-de Gennes potential; the argument relies on this for the energy estimates and is explicitly restricted to it via the uniaxial reduction shown in the last section.

C3one line summary

Existence of weak solutions satisfying natural bounds and an expanded Leray-Hopf energy inequality is proved for the 3D Beris-Edwards system with stable Landau-de Gennes potential.

References

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[1] H. Abels, G. Dolzmann, and Y. N. Liu. Well-posedness of a fully coupled navier–stokes/q- tensor system with inhomogeneous boundary data.SIAM Journal on Mathematical Analysis, 46(4):3050–3077, 2014 2014

[2] J.-P. Aubin. Un th´ eor` eme de compacit´ e.Comptes Rendus de l’Acad´ emie des Sciences Paris, 256:5042–5044, 1963 1963

[3] J. M. Ball and A. Majumdar. Nematic liquid crystals: from maier–saupe to a continuum theory.Molecular Crystals and Liquid Crystals, 525(1):1–11, 2010 2010

[4] A. N. Beris and B. J. Edwards.Thermodynamics of Flowing Systems with Internal Microstruc- ture. Oxford University Press, 1994 1994

[5] A. P. Calder´ on and A. Zygmund.Singular Integral Operators and Differential Properties of Functions. University of Chicago, 1952 1952

Receipt and verification

First computed	2026-05-20T00:03:35.133412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

daeb4a348653cafba63a5b0cbaa462714d73a3d2029685c65ee4c66078e379aa

Aliases

arxiv: 2605.16997 · arxiv_version: 2605.16997v1 · doi: 10.48550/arxiv.2605.16997 · pith_short_12: 3LVUUNEGKPFP · pith_short_16: 3LVUUNEGKPFPXJR2 · pith_short_8: 3LVUUNEG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3LVUUNEGKPFPXJR2LMGLVJDCOF \
  | 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: daeb4a348653cafba63a5b0cbaa462714d73a3d2029685c65ee4c66078e379aa

Canonical record JSON

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    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-16T13:44:33Z",
    "title_canon_sha256": "35ce6f70b1f32d83d5991b43e4bc22c7098aeee77c75932d21dd9f9549b57f4b"
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    "kind": "arxiv",
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