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 ∥uin∥Hs+1 + ∥ϑin∥Hs+2 ≤ ∊0ν½, then the asymptotic stability holds.
Original language | English (US) |
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Pages (from-to) | 1284-1318 |
Number of pages | 35 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 55 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2023 |
Keywords
- Couette flow
- Navier-Stokes Boussinesq
- large Richardson number
- stability threshold
ASJC Scopus subject areas
- Analysis
- Computational Mathematics
- Applied Mathematics