Pith. Sign in

RECORD

Local existence of classical solutions to the 3D isentropic compressible Navier-Stokes-Poisson equations with degenerate viscosities and vacuum

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Peng Lu, Shaojun Yu

Analysis of PDEs · Submitted 22 Jul 2024

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

The authors' main claim The local well-posedness of classical solution is established by introducing a "quasi-symmetric hyperbolic"-"degenerate elliptic" coupled structure to control the behavior of the velocity of the fluid near the vacuum and give some uniform estimates.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2407.15897 (version 1)
Pith IDODBYECXS, Pith's permanent record of this paper and its review
CitationPeng Lu, Shaojun Yu. "Local existence of classical solutions to the 3D isentropic compressible Navier-Stokes-Poisson equations with degenerate viscosities and vacuum." arXiv:2407.15897 (2024). https://pith.science/paper/ODBYECXS
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,014 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.50 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We consider the isentropic compressible Navier-Stokes-Poisson equations with degenerate viscousities and vacuum in a three-dimensional torus. The local well-posedness of classical solution is established by introducing a "quasi-symmetric hyperbolic"-"degenerate elliptic" coupled structure to control the behavior of the velocity of the fluid near the vacuum and give some uniform estimates. In particular, the initial data allows vacuum in an open set and we do not need any initial compatibility conditions.

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 isentropic compressible Navier-Stokes-Poisson equations with degenerate viscousities and vacuum in a three-dimensional torus. background 0.86 0.53 0.03 asserted 0.54
s1 The local well-posedness of classical solution is established by introducing a "quasi-symmetric hyperbolic"-"degenerate elliptic" coupled structure to control the behavior of the velocity of the fluid near the vacuum and give some uniform estimates. contribution 0.47 0.95 0.90 asserted 1.00
s2 In particular, the initial data allows vacuum in an open set and we do not need any initial compatibility conditions. result 0.84 0.89 0.12 asserted 0.99

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 v1
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 isentropic compressible Navier-Stokes-Poisson equations with degenerate viscousities and vacuum in a three-dimensional torus. The local well-posedness of classical solution is established by introducing a "quasi-symmetric hyperbolic"-"degenerate elliptic" coupled structure to control the behavior of the velocity of the fluid near the vacuum and give some uniform estimates. In particular, the initial data allows vacuum in an open set and we do not need any initial compatibility conditions.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.