On the stability problem of stationary solutions for the euler equation on a 2-dimensional torus |
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Authors: | P Buttà P Negrini |
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Institution: | 1.Dipartimento di Matematica,SAPIENZA Università di Roma,Roma,Italy |
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Abstract: | 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. |
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