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math.DS2003
Generic hydrodynamic instability of curl eigenfields
John B. Etnyre, Robert Ghrist
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 i…
math.DS1999
Stratified integrals and unknots in invisid flows
John B. Etnyre, Robert W. Ghrist
We prove that any steady solution to the real analytic Euler equations on a Riemannian 3-sphere must possess a periodic orbit bounding an embedded disc. One key ingredient is an ex…
math.DS1999
Gradient flows within plane fields
John Etnyre, Robert Ghrist
We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such…