Pith Number

pith:GCLFKPKV

pith:2026:GCLFKPKVCVB35Z3UCLBGYS7NBN

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Entropy Structures and Long-Time Relaxation for 3-Wave Kinetic Equations

Gigliola Staffilani, Minh-Binh Tran

A one-sided algebraic balance condition on interaction weights generates new entropy structures that produce global weak L1_loc solutions to three-wave kinetic equations and force local relaxation to zero as time tends to infinity.

arxiv:2605.10788 v2 · 2026-05-11 · math.AP · math-ph · math.MP

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Claims

C1strongest claim

We establish a new class of entropy structures for 3-wave kinetic equations with a broad family of interaction weights. ... these estimates form the central a priori mechanism of the paper and are the key ingredient in the construction of global weak L1_loc solutions. We also prove a long-time rigidity result, showing that the solutions obtained by this entropy compactness method relax locally to the zero equilibrium as t→∞.

C2weakest assumption

The interaction weights satisfy a one-sided algebraic balance condition that is sufficient to generate the new entropy structures and close the estimates.

C3one line summary

New entropy structures from one-sided balance conditions on interaction weights yield global weak L1_loc solutions to 3-wave kinetic equations and prove their local relaxation to zero equilibrium.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Global time-analytic strong solutions for a class of 3-wave kinetic equations

Receipt and verification

First computed	2026-07-16T00:21:48.145205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3096553d551543bee77412c26c4bed0b4e64816a1752d07ab4229a1ef34ebdf6

Aliases

arxiv: 2605.10788 · arxiv_version: 2605.10788v2 · doi: 10.48550/arxiv.2605.10788 · pith_short_12: GCLFKPKVCVB3 · pith_short_16: GCLFKPKVCVB35Z3U · pith_short_8: GCLFKPKV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GCLFKPKVCVB35Z3UCLBGYS7NBN \
  | 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: 3096553d551543bee77412c26c4bed0b4e64816a1752d07ab4229a1ef34ebdf6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a099daafee44d0190f1a0bfd571256a2ba476423819fa43f3703ba2226b17ab",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-11T16:20:59Z",
    "title_canon_sha256": "d4ccc1d80127afcee66b33eea4613cd7271697e315d4cb885ca9e37b11bf265b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10788",
    "kind": "arxiv",
    "version": 2
  }
}