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On the Arnol’d stability criterion for steady-state flows of an ideal fluid. (English) Zbl 0742.76038
Summary: It is proved that, in contrast to the 2-D case, the sufficient Arnol’d stability criterion for steady-state solutions of the incompressible Euler equations is never satisfied when 3-D perturbations are considered.

MSC:
76E30 Nonlinear effects in hydrodynamic stability
76B99 Incompressible inviscid fluids
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