Pith Number

pith:RNJYUIP6

pith:2026:RNJYUIP6IN3DSGAV2YQGM4AJIS

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Well-posedness of the obstacle problem for generalized Dean-Kawasaki equation

Rangrang Zhang, Ruoyang Liu

Obstacle problems for generalized Dean-Kawasaki equations admit well-posed stochastic kinetic solutions under continuous obstacles.

arxiv:2605.15501 v1 · 2026-05-15 · math.PR · math.AP

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Claims

C1strongest claim

Under a merely continuous obstacle and the same structural assumptions as in the obstacle-free setting, we obtain well-posedness over the full porous-medium regime, covering degenerate diffusion and the critical square-root noise coefficient.

C2weakest assumption

The kinetic characterization of the Skorokhod condition combined with the barrier substituting the solution yields a stable framework adapted to the L1 doubling of variables method.

C3one line summary

Proves well-posedness of the obstacle problem for generalized Dean-Kawasaki equations via kinetic formulation of the reflection term, covering the full porous-medium regime under continuous obstacles.

References

52 extracted · 52 resolved · 0 Pith anchors

[1] Quasilinear elliptic-parabolic differential equations.Math 1983

[2] Sebastian Andres and Max-K. von Renesse. Particle approximation of the Wasserstein diffusion.J. Funct. Anal., 258(11):3879–3905, 2010 2010

[3] C Anthony J Appelo and Dieke Postma.Geochemistry, groundwater and pollution. CRC press, 2004 2004

[4] Parabolic obstacle problems, quasi- convexity and regularity.Ann 2019

[5] Simulation of reactive transport in fractured porous media.Transp 2023

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:01.893705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b538a21fe4376391815d620667009449c7ec5d0406d2da15acbc922ca29581b

Aliases

arxiv: 2605.15501 · arxiv_version: 2605.15501v1 · doi: 10.48550/arxiv.2605.15501 · pith_short_12: RNJYUIP6IN3D · pith_short_16: RNJYUIP6IN3DSGAV · pith_short_8: RNJYUIP6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RNJYUIP6IN3DSGAV2YQGM4AJIS \
  | 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: 8b538a21fe4376391815d620667009449c7ec5d0406d2da15acbc922ca29581b

Canonical record JSON

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    "abstract_canon_sha256": "db5497cc57100e655d219ddb330275368a64b4a6838df4fc2f19446920a4419f",
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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-15T00:37:01Z",
    "title_canon_sha256": "314b4e4e5bd88e02f8caa9ff6305c74713551c98383dac840f5693755be69537"
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