Pith Number

pith:OGCEDUDT

pith:2026:OGCEDUDT77LL2KFZBBQDH2XTQR

not attested not anchored not stored refs pending

Instantaneous blowup of incompressible flow with passive tracer

Mimi Dai, Xiaotong "Dawson" Yang

Solutions to incompressible flow with a passive tracer can blow up instantaneously in both velocity and tracer at a finite time while remaining smooth at all other times.

arxiv:2604.11769 v2 · 2026-04-13 · math.AP

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\pithnumber{OGCEDUDT77LL2KFZBBQDH2XTQR}

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We construct a family of solutions (u,b) of the incompressible flow with a passive tracer for which both ||u(t)||_{L^∞} and ||b(t)||_{L^∞} blow up at time T_*. Away from T_*, the solutions remain smooth in both space and time.

C2weakest assumption

The iteration must propagate the tracer while preserving the same principal velocity profiles from one stage to the next; this compatibility constraint is resolved by introducing a simultaneous decomposition lemma for a symmetric tensor and a vector field.

C3one line summary

Solutions to incompressible flow with passive tracer are constructed that blow up instantaneously in L^∞ for both velocity and tracer at finite time T_* while remaining smooth before.

Receipt and verification

First computed	2026-06-02T03:04:41.158791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

718441d073ffd6bd28b9086033eaf384404de35320538f198f46053b25cd0a42

Aliases

arxiv: 2604.11769 · arxiv_version: 2604.11769v2 · doi: 10.48550/arxiv.2604.11769 · pith_short_12: OGCEDUDT77LL · pith_short_16: OGCEDUDT77LL2KFZ · pith_short_8: OGCEDUDT

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OGCEDUDT77LL2KFZBBQDH2XTQR \
  | 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: 718441d073ffd6bd28b9086033eaf384404de35320538f198f46053b25cd0a42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28507c45e3d14bd9eee1fe1c0899b73a207e57171b27360fbd050808ed783788",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-04-13T17:40:23Z",
    "title_canon_sha256": "3b4baf92579dc9eb8699ccdb38c23517c0f1907762fdb70b6234c336690fce5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.11769",
    "kind": "arxiv",
    "version": 2
  }
}