Abstract
This talk is on a problem in mathematical hydrodynamics. The speaker will describe a phenomenon observed in solutions of the Euler equations of hydrodynamics, in a setting with a strong analogy to Hamiltonian dynamical systems. The analysis will address 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 a theory of periodic and quasi-periodic orbits via a version of KAM theory, and a topological principle to count multiplicity of solutions. This is ongoing joint work with C. Garcia (McMaster) and C. R. Yang (Fields Institute).
About the speaker
Prof Walter Craig received his PhD from the Courant Institute in 1981. He taught at Caltech, Stanford and Brown University before he joined McMaster University in 2000, where he is currently Professor and Canada Research Chair of Mathematical Analysis and its Applications. He has been appointed Director of the Fields Institute for Research in Mathematical Sciences since July 2013.
Prof Craig's research focuses on nonlinear partial differential equations, Hamiltonian dynamical systems, fluid dynamics and quantum mechanics. His contributions have been to theoretical aspects of these fields, as well as their applications to fundamental problems in physics; these include small divisor problems in Hamiltonian partial differential equations, microlocal propagation of singularities for the Schrodinger equation, advances in the mathematical theory of water waves and their modeling, and progress on the important issue of regularity for solutions of the Navier - Stokes equations. He has authored more than 100 research articles and been in the editorial board in many leading journals including Communications in Contemporary Mathematics, Journal of Dynamics and Differential Equations and Mathematical Physics Electronic Journal.
Prof Craig has been awarded a Bantrell, an Alfred P. Sloan and a Killam Research Fellowships, and was elected as a Fellow of the Royal Society of Canada, of the American Association for the Advancement of Science and American Mathematical Society, as well as a Fields Institute Fellow.
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