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The inviscid limit for two-dimensional incompressible fluids with unbounded vorticity

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James P. Kelliher

Mathematical Physics · Submitted 3 Sep 2004

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

The authors' main claim We combine these two approaches to establish, in the plane, the uniqueness of solutions to the Euler equations and the same zero-viscosity convergence as Chemin, but under Yudovich's assumptions on the vorticity with q = 2.

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arXiv IDmath-ph/0409011 (version 1)
Pith IDXYA56FBO, Pith's permanent record of this paper and its review
CitationJames P. Kelliher. "The inviscid limit for two-dimensional incompressible fluids with unbounded vorticity." arXiv:math-ph/0409011 (2004). https://pith.science/paper/XYA56FBO
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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, 3,858 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.52 · compares with prior results 0.96 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Chemin has shown that solutions of the Navier-Stokes equations in the plane for an incompressible fluid whose initial vorticity is bounded and lies in L^2 converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler equations, convergence being uniform over any finite time interval. Yudovich, assuming an initial vorticity lying in L^p for all p >= q for some q, established the uniqueness of solutions to the Euler equations for an incompressible fluid in a bounded domain of n-space assuming a particular bound on the growth of the L^p-norm of the initial vorticity as p grows large. We combine these two approaches to establish, in the plane, the uniqueness of solutions to the Euler equations and the same zero-viscosity convergence as Chemin, but under Yudovich's assumptions on the vorticity with q = 2. The resulting bounded rate of convergence can be arbitrarily slow as a function of the viscosity.

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 Chemin has shown that solutions of the Navier-Stokes equations in the plane for an incompressible fluid whose initial vorticity is bounded and lies in L^2 converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler equations, convergence being uniform over any finite time interval. background 1.00 0.02 0.04 asserted 1.00
s1 Yudovich, assuming an initial vorticity lying in L^p for all p >= q for some q, established the uniqueness of solutions to the Euler equations for an incompressible fluid in a bounded domain of n-space assuming a particular bound on the growth of the L^p-norm of the initial vorticity as p grows large. background 1.00 0.03 0.03 asserted 1.00
s2 We combine these two approaches to establish, in the plane, the uniqueness of solutions to the Euler equations and the same zero-viscosity convergence as Chemin, but under Yudovich's assumptions on the vorticity with q = 2. contribution 0.88 0.95 0.91 asserted 1.00
s3 The resulting bounded rate of convergence can be arbitrarily slow as a function of the viscosity. limitation 0.54 0.84 0.08 asserted 0.93

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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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

Chemin has shown that solutions of the Navier-Stokes equations in the plane for an incompressible fluid whose initial vorticity is bounded and lies in L^2 converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler equations, convergence being uniform over any finite time interval. Yudovich, assuming an initial vorticity lying in L^p for all p >= q for some q, established the uniqueness of solutions to the Euler equations for an incompressible fluid in a bounded domain of n-space assuming a particular bound on the growth of the L^p-norm of the initial vorticity as p grows large. We combine these two approaches to establish, in the plane, the uniqueness of solutions to the Euler equations and the same zero-viscosity convergence as Chemin, but under Yudovich's assumptions on the vorticity with q = 2. The resulting bounded rate of convergence can be arbitrarily slow as a function of the viscosity.

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