Pith Number

pith:JECDWCZR

pith:2026:JECDWCZRQDRKFFQF46D2PCIADN

not attested not anchored not stored refs pending

Large data global well-posedness for a one-dimensional quasilinear wave equation

Yuusuke Sugiyama

The quasilinear wave equation u_tt = c(u)^2 u_xx has globally smooth solutions for large initial data when c is positive, bounded, monotonically increasing, and has bounded derivative.

arxiv:2605.01814 v2 · 2026-05-03 · 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{JECDWCZRQDRKFFQF46D2PCIADN}

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 prove global well-posedness for the one-dimensional quasilinear wave equation u_tt = c(u)^2 u_xx, where c is a positive, bounded, monotonically increasing function with bounded derivative. This result gives a partial resolution of an open problem posed by Glassey, Hunter and Zheng on the global existence of smooth solutions to this equation for large initial data.

C2weakest assumption

The proof relies on upper and lower estimates for the Riemann variables via a new comparison principle that exploits the monotonicity and boundedness of c; if this comparison principle fails to hold under the stated assumptions on c, the global existence claim does not follow.

C3one line summary

Global well-posedness is proved for the quasilinear wave equation u_tt = c(u)^2 u_xx under the stated conditions on c, partially resolving an open problem on large-data global existence.

Receipt and verification

First computed	2026-05-20T01:05:15.157879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49043b0b3180e2a29605e787a789001b5b574f6118567981db95b24417fb1031

Aliases

arxiv: 2605.01814 · arxiv_version: 2605.01814v2 · doi: 10.48550/arxiv.2605.01814 · pith_short_12: JECDWCZRQDRK · pith_short_16: JECDWCZRQDRKFFQF · pith_short_8: JECDWCZR

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/JECDWCZRQDRKFFQF46D2PCIADN \
  | 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: 49043b0b3180e2a29605e787a789001b5b574f6118567981db95b24417fb1031

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14b9bd6db9d45496cefea94935aa25743a4c7bcb95c5d2cbe1161bfd89cbc3a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-03T10:46:49Z",
    "title_canon_sha256": "fff148f9812ecd7a17a9eb528f02d8f09ee3a8eb25bb797b133f81fd8bee2152"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.01814",
    "kind": "arxiv",
    "version": 2
  }
}