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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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