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On existence of thermally coupled incompressible flows in a system of three dimensional pipes

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Michal Beneš, Igor Pažanin

Analysis of PDEs · Submitted 5 Nov 2014

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

The authors' main claim The present analysis is devoted to the proof of the existence of weak solutions for the above problem.

how it is stated · asserted 0.98 read the record →

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arXiv ID1411.1230 (version 1)
Pith IDGIMVBFO7, Pith's permanent record of this paper and its review
CitationIgor Pa\v{z}anin, Michal Bene\v{s}. "On existence of thermally coupled incompressible flows in a system of three dimensional pipes." arXiv:1411.1230 (2014). https://pith.science/paper/GIMVBFO7
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,257 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in a system of three-dimensional pipes on a time interval $(0,T)$. Here we are motivated by the bounded domain approach with "do-nothing" boundary conditions. In terms of the velocity, pressure and enthalpy of the fluid, such flows are described by a parabolic system with strong nonlinearities and including the artificial boundary conditions for the velocity and nonlinear boundary conditions for the so called enthalpy of the fluid. The present analysis is devoted to the proof of the existence of weak solutions for the above problem. In addition, we deal with some regularity for the velocity of the fluid.

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 study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in a system of three-dimensional pipes on a time interval $(0,T)$. contribution 0.75 0.82 0.03 asserted 0.80
s1 Here we are motivated by the bounded domain approach with "do-nothing" boundary conditions. background 0.50 0.16 0.02 asserted 0.91
s2 In terms of the velocity, pressure and enthalpy of the fluid, such flows are described by a parabolic system with strong nonlinearities and including the artificial boundary conditions for the velocity and nonlinear boundary conditions for the so called enthalpy of the fluid. method 0.51 0.33 0.04 asserted 1.00
s3 The present analysis is devoted to the proof of the existence of weak solutions for the above problem. contribution 0.84 0.91 0.82 asserted 0.98
s4 In addition, we deal with some regularity for the velocity of the fluid. contribution 0.79 0.91 0.06 asserted 0.87

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

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  • 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 study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in a system of three-dimensional pipes on a time interval $(0,T)$. Here we are motivated by the bounded domain approach with "do-nothing" boundary conditions. In terms of the velocity, pressure and enthalpy of the fluid, such flows are described by a parabolic system with strong nonlinearities and including the artificial boundary conditions for the velocity and nonlinear boundary conditions for the so called enthalpy of the fluid. The present analysis is devoted to the proof of the existence of weak solutions for the above problem. In addition, we deal with some regularity for the velocity of the fluid.

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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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