Pith Number

pith:PF4DXCLV

pith:2026:PF4DXCLVUNWIEJ3CHEBF3WQ6AS

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Global well-posedness and decay rates for the three dimensional incompressible active liquid crystals

Fan Yang, Xiongfeng Yang

Global strong solutions exist for the 3D active liquid crystal system when initial data are small and activity exceeds a critical threshold.

arxiv:2605.04625 v2 · 2026-05-06 · math.AP

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Claims

C1strongest claim

Existence and uniqueness of global strong solutions for small initial data (Q0,u0) in H^{s+1} x H^s (s>=2) when activity c > c_star, together with a mixing decay estimate on partial^k Q(t) that combines exponential decay at rate proportional to (c - c_star) Gamma and the optimal algebraic heat-kernel rate for k <= s-1.

C2weakest assumption

The initial data must be sufficiently small in the indicated Sobolev norms and the activity must exceed the critical threshold c_star; the proof relies on this smallness to close the a priori estimates via refined commutator bounds.

C3one line summary

Global well-posedness for small data and activity-dependent decay rates are established for the 3D Beris-Edwards active liquid crystal system using commutator estimates and Green's functions.

References

69 extracted · 69 resolved · 1 Pith anchors

[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, 2014, 46(4): 3050–3077 2014

[2] H. Abels, G. Dolzmann and Y . N. Liu,Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions, Advances in Differential Equations, 2016, 2016

[3] De Anna,A global 2D well-posedness result on the order tensor liquid crystal theory, Journal of Differential Equations, 2017, 262(7): 3932–3979 2017

[4] De Anna and A 2016

[5] J. M. Ball and A. Majumdar,Nematic liquid crystals: from Maier-Saupe to a continuum theory, Molecular crystals and liquid crystals, 2010, 525(1): 1–11 2010

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:40.689362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79783b8975a36c82276239025dda1e0498613967dc18cd1b7adf25c9d366639d

Aliases

arxiv: 2605.04625 · arxiv_version: 2605.04625v2 · doi: 10.48550/arxiv.2605.04625 · pith_short_12: PF4DXCLVUNWI · pith_short_16: PF4DXCLVUNWIEJ3C · pith_short_8: PF4DXCLV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PF4DXCLVUNWIEJ3CHEBF3WQ6AS \
  | 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: 79783b8975a36c82276239025dda1e0498613967dc18cd1b7adf25c9d366639d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "201c5b4745aa4da60f4598251c52eaff87e56348682e61a525a8f1dda3bf3e2f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-06T08:13:36Z",
    "title_canon_sha256": "1b51ee3962d2b956cfd432dbafaeb77780bb0b357dda55845c89180cd93a8b5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04625",
    "kind": "arxiv",
    "version": 2
  }
}