A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid

Yoshitaka Watanabe

doi:10.1016/j.cam.2008.03.034

A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid

Yoshitaka Watanabe

研究成果: Contribution to journal › Article › 査読

9 被引用数 (Scopus)

抄録

A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations.

本文言語	英語
ページ（範囲）	953-966
ページ数	14
ジャーナル	Journal of Computational and Applied Mathematics
巻	223
号	2
DOI	https://doi.org/10.1016/j.cam.2008.03.034
出版ステータス	出版済み - 1 15 2009

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

文献へのアクセス

10.1016/j.cam.2008.03.034

フィンガープリント「A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル

@article{a3411655267c465fa1b9dd6b54c84d5b,

title = "A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid",

abstract = "A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations.",

author = "Yoshitaka Watanabe",

year = "2009",

month = jan,

day = "15",

doi = "10.1016/j.cam.2008.03.034",

language = "English",

volume = "223",

pages = "953--966",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid

AU - Watanabe, Yoshitaka

PY - 2009/1/15

Y1 - 2009/1/15

N2 - A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations.

AB - A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations.

UR - http://www.scopus.com/inward/record.url?scp=56949087917&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56949087917&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2008.03.034

DO - 10.1016/j.cam.2008.03.034

M3 - Article

AN - SCOPUS:56949087917

VL - 223

SP - 953

EP - 966

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -