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From anisotropic Navier-Stokes equations to primitive equations for the ocean and atmosphere

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Valentin Lemarié (LAMA)

Analysis of PDEs · Submitted 3 Jun 2024

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

The authors' main claim Then, in a second step, we rigorously justify the passage to the limit from the rescaled anisotropic Navier-Stokes equations to these primitive equations in the same functional framework as that found for the solutions of the primitive equations.

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arXiv ID2406.01104 (version 1)
Pith IDY2X3BYNF, Pith's permanent record of this paper and its review
CitationValentin Lemari\'e (LAMA). "From anisotropic Navier-Stokes equations to primitive equations for the ocean and atmosphere." arXiv:2406.01104 (2024). https://pith.science/paper/Y2X3BYNF
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,082 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.09 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We study the well-posedness of the primitive equations for the ocean and atmosphere on two particular domains : a bounded domain $\Omega_1 := (-1, 1)^3$ with periodic boundary conditions and the strip $\Omega_2 := \mathbb{R}^2 \times (-1, 1)$ with a periodic boundary condition for the vertical coordinate. An existence theorem for global solutions on a suitable Besov space is derived. Then, in a second step, we rigorously justify the passage to the limit from the rescaled anisotropic Navier-Stokes equations to these primitive equations in the same functional framework as that found for the solutions of the primitive equations.

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 the well-posedness of the primitive equations for the ocean and atmosphere on two particular domains : a bounded domain $\Omega_1 := (-1, 1)^3$ with periodic boundary conditions and the strip $\Omega_2 := \mathbb{R}^2 \times (-1, 1)$ with a periodic boundary condition for the vertical coordinate. contribution 0.91 0.77 0.05 asserted 0.89
s1 An existence theorem for global solutions on a suitable Besov space is derived. result 0.93 0.94 0.30 asserted 1.00
s2 Then, in a second step, we rigorously justify the passage to the limit from the rescaled anisotropic Navier-Stokes equations to these primitive equations in the same functional framework as that found for the solutions of the primitive equations. contribution 0.66 0.94 0.53 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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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 the well-posedness of the primitive equations for the ocean and atmosphere on two particular domains : a bounded domain $\Omega_1 := (-1, 1)^3$ with periodic boundary conditions and the strip $\Omega_2 := \mathbb{R}^2 \times (-1, 1)$ with a periodic boundary condition for the vertical coordinate. An existence theorem for global solutions on a suitable Besov space is derived. Then, in a second step, we rigorously justify the passage to the limit from the rescaled anisotropic Navier-Stokes equations to these primitive equations in the same functional framework as that found for the solutions of the primitive equations.

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