STABILITY THRESHOLD OF THE COUETTE FLOW FOR NAVIER-STOKES BOUSSINESQ SYSTEM WITH LARGE RICHARDSON NUMBER γ2 > ½

Cuili Zhai, Weiren Zhao

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the nonlinear asymptotic stability of the Couette flow in the stably stratified regime, namely, the Richardson number γ2 > ½. Precisely, we prove that if the initial perturbation (uin, ϑin) of the Couette flow vs = (y, 0) and the linear temperature ρs = -γ2y + 1 satisfies ∥uinHs+1 + ∥ϑinHs+2 ≤ ∊0ν½, then the asymptotic stability holds.

Original languageEnglish (US)
Pages (from-to)1284-1318
Number of pages35
JournalSIAM Journal on Mathematical Analysis
Volume55
Issue number2
DOIs
StatePublished - Apr 2023

Keywords

  • Couette flow
  • Navier-Stokes Boussinesq
  • large Richardson number
  • stability threshold

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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