论文标题
关于无粘性boussinesq方程的稳定性估计
On stability estimates for the inviscid Boussinesq equations
论文作者
论文摘要
我们考虑剪切流量$ v =（y，0）$的组合和分层温度$θ=αy$的（$α> \ frac {1} {4} {4} $的组合，我们考虑了Inviscid 2D Boussinesq方程的（IN）稳定性问题。我们表明，对于任何$ε> 0 $，都存在非平凡的显式解决方案，最初是大小$ε$的扰动，并在时间尺度上生长到尺寸$ 1 $ $ε^{ - 2} $。此外，这些非平凡状态周围的（简化的）线性化问题在大小的频率大小上显示了上限的上限，大小。
We consider the (in)stability problem of the inviscid 2D Boussinesq equations near a combination of a shear flow $v=(y,0)$ and a stratified temperature $θ=αy$ with $α>\frac{1}{4}$. We show that for any $ε>0$ there exist non-trivial explicit solutions, which are initially perturbations of size $ε$, and grow to size $1$ on a time scale $ε^{-2}$. Moreover, the (simplified) linearized problem around these non-trivial states exhibits improved upper bounds on the possible size of norm inflation for frequencies larger and smaller than $ε^{-4}$.
