Pith Number

pith:XTZCIMHX

pith:2026:XTZCIMHX42CY4VMNEHV5ZIWT4S

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Infinite time blow-up and slow decay for the six dimensional energy-critical heat equation with self-similarly decaying initial data

Erbol Zhanpeisov, Jin Takahashi, Kotaro Hisa

The six-dimensional energy-critical heat equation with self-similar initial decay admits sign-changing solutions that blow up only after infinite time and nonnegative solutions whose decay is strictly slower than self-similar.

arxiv:2604.20396 v2 · 2026-04-22 · math.AP

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\usepackage{pith}
\pithnumber{XTZCIMHX42CY4VMNEHV5ZIWT4S}

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4 Citations open

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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

Our main result shows the existence of sign-changing solutions that exhibit infinite-time blow-up and nonnegative solutions that decay strictly more slowly than the self-similar rate. Moreover, the blow-up and decay rates are not uniquely determined by the decay rate of the initial data, but exhibit a certain flexibility depending on the construction.

C2weakest assumption

The gluing of suitably rescaled bubbles to forward self-similar solutions can be carried out rigorously for initial data with the given self-similar decay, without destroying the desired long-time behavior.

C3one line summary

Existence of infinite-time blow-up sign-changing solutions and slower-than-self-similar decaying nonnegative solutions for the 6D energy-critical heat equation with self-similarly decaying initial data.

Receipt and verification

First computed	2026-06-05T01:15:23.728703Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcf22430f7e6858e558d21ebdca2d3e4b954d5007b3fa9eeb86aecdc6ead20a9

Aliases

arxiv: 2604.20396 · arxiv_version: 2604.20396v2 · doi: 10.48550/arxiv.2604.20396 · pith_short_12: XTZCIMHX42CY · pith_short_16: XTZCIMHX42CY4VMN · pith_short_8: XTZCIMHX

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XTZCIMHX42CY4VMNEHV5ZIWT4S \
  | 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: bcf22430f7e6858e558d21ebdca2d3e4b954d5007b3fa9eeb86aecdc6ead20a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "678ba1263fa46fdb0713469f772a718b262e063882f438ede821bf9c1605326a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-04-22T09:59:14Z",
    "title_canon_sha256": "dcd12033c2ba1c58b5f2510c3cd12f75e9d01182d3cd93077fb8aedffef5095d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.20396",
    "kind": "arxiv",
    "version": 2
  }
}