论文标题
粘性液体的稳态流动的非线性光谱不稳定经过旋转障碍物
Nonlinear spectral instability of steady-state flow of a viscous liquid past a rotating obstacle
论文作者
论文摘要
我们表明，如果相关的线性操作员$ \ cal l $具有半Plane$ \ {λ\ in \ mathbb c; c; \ \ re} $ re} $ re} $ re} $ re} $ re} $ re的稳态解决方案$ {\ bf u} $，向旋转体的方程式系统流过一个旋转体的方程系统是不稳定的。我们的结果并非来自已知方法，在光谱不稳定性上％，主要是因为基本的非线性操作员在研究不稳定的同一空间中没有界定。作为独立利息的辅助结果，我们还表明，$ c_0 $ - semigroup $ {\ rm e}^{{{\ cal l} t} $的统一增长界限等于运算符$ \ Mathcal l $的频谱。
We show that a steady-state solution ${\bf U}$ to the system of equations of a Navier-Stokes flow past a rotating body is nonlinearly unstable if the associated linear operator $\cal L$ has a part of the spectrum in the half-plane $\{λ\in\mathbb C;\ {\rm Re}\, λ>0\}$. Our result does not follow from known methods, %on spectral instability, mainly because the basic nonlinear operator is not bounded in the same space in which the instability is studied. As an auxiliary result of independent interest, we also show that the uniform growth bound of the $C_0$--semigroup ${\rm e}^{{\cal L} t}$ is equal to the spectral bound of operator $\mathcal L$.
