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A regularization of incompressible Stokes problem with Tresca friction condition

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A. Zafrar

Analysis of PDEs · Submitted 28 Feb 2025

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

The authors' main claim We use a fixed point strategy to show the existence and uniqueness of a solution and we reformulate the problem as an equivalent constrained minimization problem.

how it is stated · asserted 1.00 read the record →

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arXiv ID2503.00158 (version 1)
Pith IDRBFUS2PK, Pith's permanent record of this paper and its review
CitationA. Zafrar. "A regularization of incompressible Stokes problem with Tresca friction condition." arXiv:2503.00158 (2025). https://pith.science/paper/RBFUS2PK
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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, 3,630 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.05 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

In the present article, we introduce and study a model addressing the Stokes problem with non-linear boundary conditions of the Tresca type. We suggest a new procedure for regularizing incompressible fluid, i.e. we assume that the divergence $\nabla \cdot {\bf u}\in [-\epsilon,\,\epsilon]$ which leads to class of constrained elliptic variational inequalities. We use a fixed point strategy to show the existence and uniqueness of a solution and we reformulate the problem as an equivalent constrained minimization problem. An ADMM is applied to the minimization problem and some algorithm are provided.

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 In the present article, we introduce and study a model addressing the Stokes problem with non-linear boundary conditions of the Tresca type. contribution 0.98 0.92 0.09 asserted 0.99
s1 We suggest a new procedure for regularizing incompressible fluid, i.e. we assume that the divergence $\nabla \cdot {\bf u}\in [-\epsilon,\,\epsilon]$ which leads to class of constrained elliptic variational inequalities. method 0.82 0.91 0.08 asserted 0.59
s2 We use a fixed point strategy to show the existence and uniqueness of a solution and we reformulate the problem as an equivalent constrained minimization problem. method 0.72 0.95 0.31 asserted 1.00
s3 An ADMM is applied to the minimization problem and some algorithm are provided. method 0.95 0.89 0.07 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.71 · 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
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  • 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

In the present article, we introduce and study a model addressing the Stokes problem with non-linear boundary conditions of the Tresca type. We suggest a new procedure for regularizing incompressible fluid, i.e. we assume that the divergence $\nabla \cdot {\bf u}\in [-\epsilon,\,\epsilon]$ which leads to class of constrained elliptic variational inequalities. We use a fixed point strategy to show the existence and uniqueness of a solution and we reformulate the problem as an equivalent constrained minimization problem. An ADMM is applied to the minimization problem and some algorithm are provided.

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