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Global well posedness for a two-fluid model

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Yoshikazu Giga, Slim Ibrahim, Shengyi Shen, Tsuyoshi Yoneda

Analysis of PDEs · Submitted 4 Nov 2014

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

The authors' main claim Regardless of the size of the initial data, we first prove the global well-posedness of the Cauchy problem when the space dimension is two.

how it is stated · asserted 1.00 read the record →

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arXiv ID1411.0917 (version 3)
Pith IDM7XIVU3G, Pith's permanent record of this paper and its review
CitationShengyi Shen, Slim Ibrahim, Tsuyoshi Yoneda, Yoshikazu Giga. "Global well posedness for a two-fluid model." arXiv:1411.0917 (2014). https://pith.science/paper/M7XIVU3G
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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, 4,887 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.82 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.96 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space dimensions two and three. Regardless of the size of the initial data, we first prove the global well-posedness of the Cauchy problem when the space dimension is two. However, in space dimension three, we construct global weak-solutions \`a la Leray, and we prove the local well-posedness of Kato-type solutions. These solutions turn out to be global when the initial data are sufficiently small. Our results extend Giga-Yoshida (1984) ones to the space dimension two, and improve them in terms of requiring less regularity on the velocity fields.

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 a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. background 0.59 0.52 0.03 asserted 0.88
s1 We study the well-posdness of the system in both space dimensions two and three. contribution 0.94 0.81 0.06 asserted 0.86
s2 Regardless of the size of the initial data, we first prove the global well-posedness of the Cauchy problem when the space dimension is two. result 0.98 0.95 0.41 asserted 1.00
s3 However, in space dimension three, we construct global weak-solutions \`a la Leray, and we prove the local well-posedness of Kato-type solutions. result 0.61 0.95 0.19 asserted 1.00
s4 These solutions turn out to be global when the initial data are sufficiently small. result 0.98 0.93 0.16 asserted 0.99
s5 Our results extend Giga-Yoshida (1984) ones to the space dimension two, and improve them in terms of requiring less regularity on the velocity fields. contribution 0.55 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.

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not examined
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  • references and citing sentences
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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

We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space dimensions two and three. Regardless of the size of the initial data, we first prove the global well-posedness of the Cauchy problem when the space dimension is two. However, in space dimension three, we construct global weak-solutions \`a la Leray, and we prove the local well-posedness of Kato-type solutions. These solutions turn out to be global when the initial data are sufficiently small. Our results extend Giga-Yoshida (1984) ones to the space dimension two, and improve them in terms of requiring less regularity on the velocity fields.

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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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