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Generic hydrodynamic instability for curl eigenfields

By John Etnyre and Robert Ghrist


ABSTRACT. We prove that for generic geometry, the curl-eigenfield solutions to the steady Euler equations on R 3 /Z 3 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. 1

Year: 2005
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