论文标题
在2D稳定分层方面的Couette附近的剪切流的线性无粘性阻尼
Linear inviscid damping for shear flows near Couette in the 2D stably stratified regime
论文作者
论文摘要
我们研究了一类不可压缩的稳定分层流体，研究了COUETTE流附近的剪切物的线性稳定性。我们的主要结果包括几乎最佳的衰减率，用于固定状态的扰动，其速度是单调剪切流$（u（y），0）$，并且具有指数密度的曲线。对于Couette Flow $ u（y）= y $，我们通过在频率空间中采用明确的点方法来恢复Hartman在1975年预测的费率。作为副产品，这意味着涡度的最佳衰减率以及$ l^2 $的Lyapunov不稳定。对于先前未开发的情况，即接近COUETTE的更通用的剪切流动，无粘性阻尼结果是加权能量估计值。关于稳定分层方案的每个结果也适用于Boussinesq方程。值得注意的是，我们的结果在著名的Miles-Howard标准下，用于分层流体。
We investigate the linear stability of shears near the Couette flow for a class of 2D incompressible stably stratified fluids. Our main result consists of nearly optimal decay rates for perturbations of stationary states whose velocities are monotone shear flows $(U(y),0)$ and have an exponential density profile. In the case of the Couette flow $U(y)=y$, we recover the rates predicted by Hartman in 1975, by adopting an explicit point-wise approach in frequency space. As a by-product, this implies optimal decay rates as well as Lyapunov instability in $L^2$ for the vorticity. For the previously unexplored case of more general shear flows close to Couette, the inviscid damping results follow by a weighted energy estimate. Each outcome concerning the stably stratified regime applies to the Boussinesq equations as well. Remarkably, our results hold under the celebrated Miles-Howard criterion for stratified fluids.
