Pith Number

pith:E5LM5FEC

pith:2026:E5LM5FECWPCDGVXW6KJ5YRWHZY

not attested not anchored not stored refs pending

Instantaneous blowup and non-uniqueness of smooth solutions of MHD

Mimi Dai

Smooth solutions to the incompressible MHD equations exist whose L^∞ norm blows up instantaneously at the critical rate.

arxiv:2604.08684 v2 · 2026-04-09 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E5LM5FECWPCDGVXW6KJ5YRWHZY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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 magnetohydrodynamic (MHD) system, the L^∞ norm of which blows up instantaneously at the critical rate. The solutions remain smooth except at the blowup time.

C2weakest assumption

A new coupled geometric lemma exists that simultaneously decomposes a symmetric tensor and a skew-symmetric tensor while preserving the same principal solution ansatz at every iterative step of the convex integration scheme.

C3one line summary

Family of smooth incompressible MHD solutions constructed with instantaneous critical-rate L^∞ blowup via inverse energy cascade and a new coupled geometric lemma in convex integration.

Cited by

1 paper in Pith

Sharp non-uniqueness of weak solutions to 2D magnetohydrodynamic equations

Receipt and verification

First computed	2026-06-02T02:04:17.257547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2756ce9482b3c43356f6f293dc46c7ce1e1bdefed316681ce26866195f9c1466

Aliases

arxiv: 2604.08684 · arxiv_version: 2604.08684v2 · doi: 10.48550/arxiv.2604.08684 · pith_short_12: E5LM5FECWPCD · pith_short_16: E5LM5FECWPCDGVXW · pith_short_8: E5LM5FEC

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/E5LM5FECWPCDGVXW6KJ5YRWHZY \
  | 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: 2756ce9482b3c43356f6f293dc46c7ce1e1bdefed316681ce26866195f9c1466

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fca947510ef049d5d9d1d28affacd36ffe8e7fa1fa5ec989c03f09acab95459",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-04-09T18:16:17Z",
    "title_canon_sha256": "f03124e585118f2150cab23c340e09c6e8be74adf7e8f4e633974ca1ede94584"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.08684",
    "kind": "arxiv",
    "version": 2
  }
}