Pith Number

pith:A6Q2IRGZ

pith:2026:A6Q2IRGZFFTOX2WHF7NWMC46SM

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Asymptotic study of supercritical generalized SQG equations in critical Sobolev spaces

Anuj Kumar

Small initial data in the critical Sobolev norm yields unique global solutions to the supercritical generalized SQG equations whose norm decays to zero over time.

arxiv:2605.13176 v1 · 2026-05-13 · math.AP

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3 Author claim open · sign in to claim

4 Citations open

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Claims

C1strongest claim

under the assumption of small initial data in the critical Sobolev norm, we prove the existence of the unique global solution that satisfies the energy inequality (1.3) and for which the critical norm ||θ(t)||_{H^{1+β-2α}} decays to 0 as time goes to infinity.

C2weakest assumption

The initial data is sufficiently small in the critical Sobolev norm H^{1+β-2α}.

C3one line summary

Small critical-norm data yield unique global solutions to supercritical gSQG equations whose critical Sobolev norm decays to zero.

References

31 extracted · 31 resolved · 0 Pith anchors

[1] M. Amara and J. Benameur. Global solution of anisotropic quasi-geostrophic equations in sobolev spaces.Journal of Mathematical Analysis and Applications, 516(1), 2022 2022

[2] H. Bahouri, J.-Y. Chemin, and R. Danchin.Fourier analysis and nonlinear partial differential equations, volume 343 ofGrundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematic 2011

[3] J. Benameur and S.B. Abdallah. Asymptotic behavior of critical dissipative quasi-geostrophic equation in fourier space.Journal of Mathematical Analysis and Applications, 497(1), 2021 2021

[4] J. Benameur and M. Benhamed. Global existence of the two-dimensional qge with sub-critical dissipation.Journal of Mathematical Analysis and Applications, 423(2), 2015 2015

[5] J. Benameur and M. Blel. Asymptotic study of the 2d-dqge solutions.Journal of Function Spaces, 2314-8896, 2014 2014

Receipt and verification

First computed	2026-05-18T03:08:56.474583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07a1a444d92966ebeac72fdb660b9e9339d936b3c8514a764ddcf6bb093179c6

Aliases

arxiv: 2605.13176 · arxiv_version: 2605.13176v1 · doi: 10.48550/arxiv.2605.13176 · pith_short_12: A6Q2IRGZFFTO · pith_short_16: A6Q2IRGZFFTOX2WH · pith_short_8: A6Q2IRGZ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/A6Q2IRGZFFTOX2WHF7NWMC46SM \
  | 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: 07a1a444d92966ebeac72fdb660b9e9339d936b3c8514a764ddcf6bb093179c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80a9b9760e68c27b03c63f4c3aa4f1de417033aae5ca11dadcfb4655b568c698",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T08:38:32Z",
    "title_canon_sha256": "f7a70a478a2a6c4f23a512eea02bf4f075089a457c417788f053b4e26a5f8bd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13176",
    "kind": "arxiv",
    "version": 1
  }
}