Rough dependence upon initial data exemplified by explicit solutions and the effect of viscosity

Y. Charles Li

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Rough dependence upon initial data exemplified by explicit solutions and the effect of viscosity

Y. Charles Li

Fluid Dynamics · Submitted 17 Jun 2015

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

The authors' main claim In this article, we present some explicit solutions showing rough dependence upon initial data.

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arXiv ID1506.05498 (version 1)

Pith IDT2NT3C76, Pith's permanent record of this paper and its review

CitationY. Charles Li. "Rough dependence upon initial data exemplified by explicit solutions and the effect of viscosity." arXiv:1506.05498 (2015). https://pith.science/paper/T2NT3C76

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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,783 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.26 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this article, we present some explicit solutions showing rough dependence upon initial data. We also studies viscous effects. An extension of a theorem of Cauchy to the viscous case is also presented.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this article, we present some explicit solutions showing rough dependence upon initial data.	contribution 0.95	0.93	0.47	asserted 1.00
s1	We also studies viscous effects.	contribution 1.00	0.86	0.08	asserted 0.90
s2	An extension of a theorem of Cauchy to the viscous case is also presented.	contribution 0.96	0.88	0.16	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 v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

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P abstract

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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

In this article, we present some explicit solutions showing rough dependence upon initial data. We also studies viscous effects. An extension of a theorem of Cauchy to the viscous case is also presented.

Human review

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How the literature uses it

3 arXiv papers cite this in 7 sentences

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

Papers citing it · 4 sentences without a confident label

Cites it as support 1 paper

Recent advances on the solution operators of Euler and Navier-Stokes equations [ref] [ref] [ref] [ref] provided enough base to evaluate the rigorous mathematical foundation of linear hydrodynamic stability theory.

Novel discoveries on the mathematical foundation of linear hydrodynamic stability theory · Introduction · 0.96

What it cites · 3 sentences without a confident label

Cites as support 1 paper

In fact, the solution operator $F^t$ is nowhere differentiable [ref] .

On the well-posedness of the incompressible Euler Equation · Explicit solutions with rough dependence on initial data · 0.97

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