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

9 引用 (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.

元の言語 英語 953-966 14 Journal of Computational and Applied Mathematics 223 2 https://doi.org/10.1016/j.cam.2008.03.034 出版済み - 1 15 2009

### Fingerprint

Computer-assisted Proof
Numerical Verification
Rounding error
Floating point
Nontrivial Solution
Viscous Fluid
Incompressible Fluid
Fixed point theorem
Uniqueness
Numerical Results
Fluids
Operator

### All Science Journal Classification (ASJC) codes

• Computational Mathematics
• Applied Mathematics

### これを引用

：: Journal of Computational and Applied Mathematics, 巻 223, 番号 2, 15.01.2009, p. 953-966.

@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 = "1",
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 -