Generic hydrodynamic instability of curl eigenfields
Joint work with Robert Ghrist.
SIAM J. Appl. Dyn. Syst. 4 (2005), no. 2, 377-390.

We prove that for generic geometry, the curl-eigenfield solutions to the steady Euler equations on the three torus are all hydrodynamically unstable (linear, $L^2$ norm). The proof involves a marriage of contact topological methods with the instability criterion of Friedlander-Vishik. An application of contact homology is the crucial step.

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