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Regularity of Leray-Hopf solutions to Navier-Stokes equations (I)-Critical interior regularity in weak spaces

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Jian Zhai

Analysis of PDEs · Submitted 30 Nov 2006

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

The authors' main claim Particularly, an open problem proposed in [KK] was solved.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0611958 (version 3)
Pith IDAHI255LY, Pith's permanent record of this paper and its review
CitationJian Zhai. "Regularity of Leray-Hopf solutions to Navier-Stokes equations (I)-Critical interior regularity in weak spaces." arXiv:math/0611958 (2006). https://pith.science/paper/AHI255LY
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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, 2,258 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.22 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We consider the interior regularity of Leray-Hopf solutions to Navier-Stokes equations on critical case L^2_w(0,T;L^\infty(R^3)). Particularly, an open problem proposed in [KK] was solved.

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 interior regularity of Leray-Hopf solutions to Navier-Stokes equations on critical case L^2_w(0,T;L^\infty(R^3)). contribution 0.73 0.70 0.14 asserted 0.51
s1 Particularly, an open problem proposed in [KK] was solved. result 0.58 0.78 0.40 asserted 1.00

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

What was examined, and what was not

sources read
  • arXiv listing abstract v3
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 interior regularity of Leray-Hopf solutions to Navier-Stokes equations on critical case L^2_w(0,T;L^\infty(R^3)). Particularly, an open problem proposed in [KK] was solved.

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