论文标题
Navier-Stokes BousSinesQ系统的COUETTE流的稳定性阈值，带有大理查森编号$γ^2> \ frac {1} {4} {4} $
Stability threshold of the Couette flow for Navier-Stokes Boussinesq system with large Richardson number $γ^2>\frac{1}{4}$
论文作者
论文摘要
在本文中，我们研究了稳定分层的couette流的非线性渐近稳定性，即理查森数量$γ^2> \ frac {1} {4} {4} $。确切地说，我们证明，如果初始扰动$（u_ {in}，\ vartheta_ {in}）$的couette flow $ v_s =（y，0）$，线性温度$ρ_S= -C.s = -Cumγ^2y+1 $满意$ \ | u_ {in} \ | _ {h^{s+1}}}+\ | \ | \ vartheta_ {in} \ | _ {h^{h^{s+2}} \ leqleqε_0ν^{\ frac {\ frac {1} {1} {2} {2}} $，然后是asmptotory stobility。
In this paper, we study the nonlinear asymptotic stability of the Couette flow in the stably stratified regime, namely the Richardson number $γ^2>\frac{1}{4}$. Precisely, we prove that if the initial perturbation $(u_{in},\vartheta_{in})$ of the Couette flow $v_s=(y,0)$ and the linear temperature $ρ_s=-γ^2y+1$ satisfies $\|u_{in}\|_{H^{s+1}}+\|\vartheta_{in}\|_{H^{s+2}}\leq ε_0ν^{\frac{1}{2}}$, then the asymptotic stability holds.
