Vortex filament dynamics

Vortex filament dynamics

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Walter Craig, The Fields Institute and McMaster University
Fine Hall 314

I will describe a a problem in mathematical hydrodynamics, in a setting with a strong analogy to Hamiltonian dynamical systems. The analysis addresses vortex filaments for the three dimensional Euler equations, and a system of model equations for the dynamics of near-parallel filaments.  These PDEs can be formulated as a Hamiltonian system, and the talk will describe some aspects of a phase space analysis of solutions, including a theory of periodic and quasi-periodic orbits via a version of KAM theory, a brief description of the relevance of Anderson localization, and a topological principle to count multiplicity of solutions. This is ongoing joint work with C. Garcia (Rome 1 - La Sapienza) and C.-R. Yang (McMaster and the Fields Institute).