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a di Roma. Abstract. We discuss the classical problem of the stability of the sta- tionary solution = cosy for the Euler equation on a 2-dimensional at torus of sides 2 L and 2 . We prove that is linearly stable if L 2 (0; 1) and that exponentially unstable modes occur in a right neighborhood of L = n for any integer n.

Stability Problems for the Euler Equation on the 2-Dimensional Torus