Paolo Butta

Piazzale Aldo Moro 2, 00185 Roma, Italy
Dipartimento di Matematica, Universita` di Roma La Sapienza


Butta P., Negrini P.
We study the linear stability problem of the stationary solution $\psi^* = −\cos y$ for the Euler equation on a 2-dimensional flat torus of sides $2\pi L$ and $2\pi$. We show that $\psi^*$ is stable if $L \in (0, 1)$ 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.
Keywords: Euler equation, shear flows, linear stability
Citation: Butta P., Negrini P.,  On the stability problem of stationary solutions for the Euler equation on a 2-dimensional torus, Regular and Chaotic Dynamics, 2010, vol. 15, no. 6, pp. 637-645
Butta P., Negrini P.
Resonances and $O$-curves in Hamiltonian systems
2007, vol. 12, no. 5, pp.  521-530
We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.
Keywords: Hamiltonian systems, resonances
Citation: Butta P., Negrini P.,  Resonances and $O$-curves in Hamiltonian systems, Regular and Chaotic Dynamics, 2007, vol. 12, no. 5, pp. 521-530

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