Pith Number

pith:RFLJGG7R

pith:2026:RFLJGG7R4674SVPZZUKARCBSYX

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Norm inflation for quadratic derivative fractional nonlinear Schr\"odinger equations

Mamoru Okamoto, Toshiki Kondo

Quadratic derivative fractional nonlinear Schrödinger equations show norm inflation with infinite regularity loss below sharp exponents, implying ill-posedness.

arxiv:2601.20294 v2 · 2026-01-28 · math.AP

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4 Citations open

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Claims

C1strongest claim

By deriving estimates for each iterated term, we establish norm inflation with infinite loss of regularity, which in particular implies ill-posedness.

C2weakest assumption

Thanks to the global well-posedness result established by Nakanishi and Wang (2025), we can expand the solution as a sum of iterated terms.

C3one line summary

For quadratic derivative fractional NLS, the Cauchy problem is ill-posed in Sobolev spaces below sharp fractional derivative exponents due to norm inflation with infinite loss of regularity.

References

26 extracted · 26 resolved · 1 Pith anchors

[1] I. Bejenaru, T. Tao,Sharp well-posedness and ill-posedness results for a quadratic non-linear Schr¨ odinger equation, J. Funct. Anal.233(2006), no. 1, 228–259 2006

[2] Chihara,The initial value problem for Schr¨ odinger equations on the torus, Int 2002

[3] Christ,Illposedness of a Schr¨ odinger equation with derivative nonlinearity, preprint (https://math.berkeley.edu/~mchrist/preprints.html)

[4] J. Chung, Z. Guo, S. Kwon, T. Oh,Normal form approach to global well-posedness of the quadratic derivative nonlinear Schr¨ odinger equation on the circle, Ann. Inst. H. Poincar´ e C Anal. Non Lin´ eai 2017

[5] On the Cauchy- and periodic boundary value problem for a certain class of derivative nonlinear Schroedinger equations · arXiv:math/0006195

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T02:04:03.663597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8956931bf1e7bfc955f9cd14088832c5f077705bfac8a0e7f734c37e4f38b226

Aliases

arxiv: 2601.20294 · arxiv_version: 2601.20294v2 · doi: 10.48550/arxiv.2601.20294 · pith_short_12: RFLJGG7R4674 · pith_short_16: RFLJGG7R4674SVPZ · pith_short_8: RFLJGG7R

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/RFLJGG7R4674SVPZZUKARCBSYX \
  | 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: 8956931bf1e7bfc955f9cd14088832c5f077705bfac8a0e7f734c37e4f38b226

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79f8e0dcace591367686f49df22a9b3e78fd1275aedad037827d21d4a57c6cf8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-01-28T06:26:46Z",
    "title_canon_sha256": "6c2cc14d6e145b295fd6357cb2dab44c2a91851eb5c080b8d6ef7e1cdba8b843"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.20294",
    "kind": "arxiv",
    "version": 2
  }
}