On the stability problem of stationary solutions for the euler equation on a 2-dimensional torus
On the stability problem of stationary solutions for the euler equation on a 2-dimensional torus
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二维环面上欧拉方程平稳解的稳定性问题
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
P. Negrini
中科院分区：
文献类型：
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作者：
P. Buttà;P. Negrini
研究了二维平面环面上欧拉方程驻定解ψ*=−cos y的线性稳定性问题，其边分别为2π、L和2π。我们证明了ψ*是稳定的，如果L∈(0，1)，并且对于任意整数n，指数不稳定模出现在L=n的右邻域内。作为推论，对于足够大的L，我们得到了指数不稳定的结果，并且随着L发散，不稳定模的数目无限增长。
We study the linear stability problem of the stationary solution ψ* = −cos y for the Euler equation on a 2-dimensional flat torus of sides 2πL and 2π. We show that ψ* is stable if L ∈ (0, 1) and that exponentially unstable modes occur in a right neighborhood of L = n for any integer n. As a corollary, we gain exponentially instability for any L large enough and an unbounded growth of the number of unstable modes as L diverges.