Abstract
We prove the absence of a real-analytic first integral in a known system describing the stationary flow of an ideal incompressible fluid with periodic boundary conditions and with velocity field collinear to the rotor of itself (an ABC-flow) for the case in which all three parameters occurring in the system are equal. A computer proof of this fact was previously known.
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Ziglin, S.L. An Analytic Proof of the Nonintegrability of the ABC-flow for A=B=C . Functional Analysis and Its Applications 37, 225–227 (2003). https://doi.org/10.1023/A:1026040802018
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DOI: https://doi.org/10.1023/A:1026040802018