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

Yoshiyuki Kagei; Wolf Von Wahl

doi:10.1512/iumj.1999.48.1613

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 journal › Article › peer-review

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 language	English
Pages (from-to)	1083-1110
Number of pages	28
Journal	Indiana University Mathematics Journal
Volume	48
Issue number	3
DOIs	https://doi.org/10.1512/iumj.1999.48.1613
Publication status	Published - 1999

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1512/iumj.1999.48.1613

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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.",

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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.

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

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