| Abstract: |
| We study the evolution of vortex filaments in ideal fluids. A conjecture, dating back to da Rios in 1906, states that if the the vorticity is intially concentrated around a closed curve, it remains concentrated for some time and the evolution of the curve is geometrically described by the binormal curvature flow. In a joint work with Bob Jerrard we focus on the second part of this conjecture and derive the binormal curvature flow under a weak vorticity concentration condition. Our proof relies on estimates for the underlying Hamiltonian structures. |
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