Nonlinear instability of ideal plane flows
Nonlinear instability of ideal plane flows
复制标题
理想平面流的非线性不稳定性
DOI：
10.1155/s107379280414018x
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发表时间：
2004
影响因子：
1
通讯作者：
Zhiwu Lin
中科院分区：
文献类型：
--
作者：
Zhiwu Lin
我们研究了静止理想平面流的非线性不稳定性。对于任何有界区域和非常一般的定常流，我们证明了如果线性化方程有指数增长的解，那么定常流是非线性不稳定的。非线性不稳定性是指我们可以找到一个任意接近定常流的初始扰动，使得速度扰动的Lp范数指数增长超过一个固定值。对Charney-Hasegawa-米马方程也证明了同样的结果。
We study nonlinear instability of stationary ideal plane flows. For any bounded domain and very general steady flows, we show that if the linearized equation has an exponentially growing solution, then the steady flow is nonlinearly unstable. The nonlinear instability is in the sense that we can find an initial perturbation arbitrarily close to the steady flow such that the L p norm of the velocity perturbation grows exponentially beyond a fixed value. The same result is also proved for the Charney-Hasegawa-Mima equation.