On the Stability Problem of Stationary Solutions for the Euler Equation on a 2-Dimensional Torus
نویسندگان
چکیده
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. MSC2010 numbers: 76E05, 35Q35, 34B08
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تاریخ انتشار 2010