### 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 language | English |
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Pages (from-to) | 1083-1110 |

Number of pages | 28 |

Journal | Indiana University Mathematics Journal |

Volume | 48 |

Issue number | 3 |

Publication status | Published - Sep 1 1999 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Indiana University Mathematics Journal*,

*48*(3), 1083-1110.

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

Research output: Contribution to journal › Article

*Indiana University Mathematics Journal*, vol. 48, no. 3, pp. 1083-1110.

}

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 -