论文标题
统一的结构稳定性和poiseuille的独特性在二维周期性带中流动
Uniform structural stability and uniqueness of Poiseuille flows in a two dimensional periodic strip
论文作者
论文摘要
在本文中，我们证明，当周期不大的情况下，在二维周期性条中，在navier-Stokes系统中，Poiseuille流动的均匀的非线性结构稳定性。关键点是通过对关联边界层的仔细分析来确定相关线性问题的先验估计。此外，即使外力在$ l^2 $中很大，也证明了Navier-Stokes系统的体系良好的理论。最后，如果垂直速度适当地小，而小速度独立于通量，那么Poiseuille流量是周期条中稳定的Navier-Stokes系统的独特解决方案。
In this paper, we prove the uniform nonlinear structural stability of Poiseuille flows with arbitrarily large flux for the Navier-Stokes system in a two dimensional periodic strip when the period is not large. The key point is to establish the a priori estimate for the associated linearized problem via the careful analysis for the associated boundary layers. Furthermore, the well-posedness theory for the Navier-Stokes system is also proved even when the external force is large in $L^2$. Finally, if the vertical velocity is suitably small where the smallness is independent of the flux, then Poiseuille flow is the unique solution of the steady Navier-Stokes system in the periodic strip.
