|タイトル||Vortex filament dynamics|
|開催日時||2016年7月13日 16:45 ～|
|講演者||Professor Walter Craig （McMaster University）|
|場所||慶應義塾大学理工学部 14棟 631A/B (創想館 6階 ミーティング1A/1B)|
The evolution of vortex filaments in three dimensions is an important problem in mathematical hydrodynamics. It appears in questions on solutions of the Euler equations as well as in the fine structure of vortex filamentation in a superfluid.
It is also a setting in the analysis of partial differential equations with a compelling analogy to Hamiltonian dynamical systems.
I will give an analysis of a system of model equations for the dynamics of near-parallel vortex filaments in a three dimensional fluid. These equations can be formulated as a Hamiltonian system of partial differential equations, and the talk will describe some aspects of a phase space analysis of solutions, including the construction of periodic and quasi-periodic orbits via a version of KAM theory for PDEs, and a topological principle to count multiplicity of solutions.
This is ongoing joint work with C. Garcia (UNAM) and C.-R. Yang (McMaster and the Fields Institute)