Pith Number

pith:EZM4P64X

pith:2026:EZM4P64XNXWAFG2N6SQ6Q3KX2Z

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Half-space problem on the Boltzmann equation with zero Mach number at infinity

Hongxu Chen, Jun-Ling Chen, Renjun Duan

Global low-regularity solutions to the half-space Boltzmann equation exist near zero-Mach Maxwellians with tangential Gevrey regularity propagating.

arxiv:2605.12914 v1 · 2026-05-13 · math.AP

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Claims

C1strongest claim

We construct global-in-time low-regularity solutions near Maxwellians... and prove the propagation of Gevrey regularity: analyticity (Gevrey index 1) in the tangential spatial variable x_∥, and Gevrey class with index 2 in the tangential velocity variable v_∥, under suitably regular initial data.

C2weakest assumption

The assumption of small perturbations around a global Maxwellian equilibrium with zero Mach number at infinity, which enables the linearization and decay estimates via macro-micro decomposition.

C3one line summary

Global solutions with heat-like decay and Gevrey regularity propagation are proven for the Boltzmann equation in half-space with zero Mach number at infinity.

References

59 extracted · 59 resolved · 0 Pith anchors

[1] R. Alexandre and C. Villani. On the Boltzmann equation for long-range interactions.Comm. Pure Appl. Math., 55(1):30–70, 2002 2002

[2] C. Bardos, R. E. Caflisch, and B. Nicolaenko. The Milne and Kramers problems for the Boltzmann equation of a hard sphere gas.Comm. Pure Appl. Math., 39(3):323–352, 1986 1986

[3] C. Bardos, F. Golse, and Y. Sone. Half-space problems for the Boltzmann equation: a survey.J. Stat. Phys., 124(2-4):275–300, 2006 2006

[4] N. Bernhoff and F. Golse. On the boundary layer equations with phase transition in the kinetic theory of gases.Arch. Ration. Mech. Anal., 240(1):51–98, 2021 2021

[5] E. Bouin, J. Dolbeault, S. Mischler, C. Mouhot, and C. Schmeiser. Hypocoercivity without confinement. Pure Appl. Anal., 2(2):203–232, 2020 2020

Receipt and verification

First computed	2026-05-18T03:09:10.393286Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2659c7fb976dec029b4df4a1e86d57d658869650403621707962542787ad8b10

Aliases

arxiv: 2605.12914 · arxiv_version: 2605.12914v1 · doi: 10.48550/arxiv.2605.12914 · pith_short_12: EZM4P64XNXWA · pith_short_16: EZM4P64XNXWAFG2N · pith_short_8: EZM4P64X

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EZM4P64XNXWAFG2N6SQ6Q3KX2Z \
  | 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: 2659c7fb976dec029b4df4a1e86d57d658869650403621707962542787ad8b10

Canonical record JSON

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    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T02:41:00Z",
    "title_canon_sha256": "7962d1327a3be06ce22ab033acb70eae5c712277a508cc01173e975000fcf312"
  },
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