Asymptotic Stability of Steady Flows in Infinite Layers of Viscous Incompressible Fluids in Critical Cases of Stability

Yoshiyuki Kagei, Wolf Von Wahl

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We investigate stability properties of the following three steady flows in an infinite fluid layer: 1. The motionless state of the Rayleigh-Bénard convection; 2. plane Couette flow in a rotating layer; and 3. plane Couette flow in a rotating layer heated from below. These steady flows are proved to be unconditionally asymptotically stable under 2-D periodic perturbations even when the control parameters reach their critical values for the linearized stability. The proof is carried out based on the Ljapunov function method.

Original languageEnglish
Pages (from-to)1083-1110
Number of pages28
JournalIndiana University Mathematics Journal
Volume48
Issue number3
Publication statusPublished - Sep 1 1999

Fingerprint

Critical Case
Steady Flow
Viscous Fluid
Incompressible Fluid
Asymptotic Stability
Couette Flow
Rotating
Unconditionally Stable
Asymptotically Stable
Rayleigh
Control Parameter
Convection
Critical value
Perturbation
Fluid

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Asymptotic Stability of Steady Flows in Infinite Layers of Viscous Incompressible Fluids in Critical Cases of Stability. / Kagei, Yoshiyuki; Von Wahl, Wolf.

In: Indiana University Mathematics Journal, Vol. 48, No. 3, 01.09.1999, p. 1083-1110.

Research output: Contribution to journalArticle

@article{4ed240fc041047e4becac278e701cf15,
title = "Asymptotic Stability of Steady Flows in Infinite Layers of Viscous Incompressible Fluids in Critical Cases of Stability",
abstract = "We investigate stability properties of the following three steady flows in an infinite fluid layer: 1. The motionless state of the Rayleigh-B{\'e}nard convection; 2. plane Couette flow in a rotating layer; and 3. plane Couette flow in a rotating layer heated from below. These steady flows are proved to be unconditionally asymptotically stable under 2-D periodic perturbations even when the control parameters reach their critical values for the linearized stability. The proof is carried out based on the Ljapunov function method.",
author = "Yoshiyuki Kagei and {Von Wahl}, Wolf",
year = "1999",
month = "9",
day = "1",
language = "English",
volume = "48",
pages = "1083--1110",
journal = "Indiana University Mathematics Journal",
issn = "0022-2518",
publisher = "Indiana University",
number = "3",

}

TY - JOUR

T1 - Asymptotic Stability of Steady Flows in Infinite Layers of Viscous Incompressible Fluids in Critical Cases of Stability

AU - Kagei, Yoshiyuki

AU - Von Wahl, Wolf

PY - 1999/9/1

Y1 - 1999/9/1

N2 - We investigate stability properties of the following three steady flows in an infinite fluid layer: 1. The motionless state of the Rayleigh-Bénard convection; 2. plane Couette flow in a rotating layer; and 3. plane Couette flow in a rotating layer heated from below. These steady flows are proved to be unconditionally asymptotically stable under 2-D periodic perturbations even when the control parameters reach their critical values for the linearized stability. The proof is carried out based on the Ljapunov function method.

AB - We investigate stability properties of the following three steady flows in an infinite fluid layer: 1. The motionless state of the Rayleigh-Bénard convection; 2. plane Couette flow in a rotating layer; and 3. plane Couette flow in a rotating layer heated from below. These steady flows are proved to be unconditionally asymptotically stable under 2-D periodic perturbations even when the control parameters reach their critical values for the linearized stability. The proof is carried out based on the Ljapunov function method.

UR - http://www.scopus.com/inward/record.url?scp=0347594324&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347594324&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0347594324

VL - 48

SP - 1083

EP - 1110

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 3

ER -