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Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity

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Lizhe Wan

Analysis of PDEs · Submitted 14 Dec 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that for $s\geq \frac{3}{4}$, the water waves system is locally well-posed in $\mathcal{H}^{s}$, which is the nonzero constant vorticity counterpart of the breakthrough work of Ai-Ifrim-Tataru in [4].

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arXiv ID2312.09347 (version 2)
Pith IDHBGFU62A, Pith's permanent record of this paper and its review
CitationLizhe Wan. "Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity." arXiv:2312.09347 (2023). https://pith.science/paper/HBGFU62A
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,010 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We consider the two dimensional gravity water waves with nonzero constant vorticity in infinite depth. We show that for $s\geq \frac{3}{4}$, the water waves system is locally well-posed in $\mathcal{H}^{s}$, which is the nonzero constant vorticity counterpart of the breakthrough work of Ai-Ifrim-Tataru in [4]. It is also a $\frac{1}{4}$ improvement in Sobolev regularity compared to the previous result of Ifrim-Tataru in [17].

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider the two dimensional gravity water waves with nonzero constant vorticity in infinite depth. background 0.88 0.22 0.02 asserted 0.74
s1 We show that for $s\geq \frac{3}{4}$, the water waves system is locally well-posed in $\mathcal{H}^{s}$, which is the nonzero constant vorticity counterpart of the breakthrough work of Ai-Ifrim-Tataru in [4]. result 0.93 0.95 0.92 asserted 1.00
s2 It is also a $\frac{1}{4}$ improvement in Sobolev regularity compared to the previous result of Ifrim-Tataru in [17]. interpretation 0.53 0.76 0.10 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider the two dimensional gravity water waves with nonzero constant vorticity in infinite depth. We show that for $s\geq \frac{3}{4}$, the water waves system is locally well-posed in $\mathcal{H}^{s}$, which is the nonzero constant vorticity counterpart of the breakthrough work of Ai-Ifrim-Tataru in [4]. It is also a $\frac{1}{4}$ improvement in Sobolev regularity compared to the previous result of Ifrim-Tataru in [17].

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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