Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Prof. Dr. Walter Craig (McMaster University, Hamilton, Ontario, Kanada)

Diese Veranstaltung ist Teil der Veranstaltungsreihe „Allgemeines Mathematisches Kolloquium“.

Abstract: The evolution of vortex filaments in three dimensions is a question of mathematical hydrodynamics and the analysis of nonlinear partial differential equations. Its applications include vortex evolution for the Euler equations as well as in the fine structure of vortex filamentation in a superfluid. It is also a setting of partial differential equations with a compelling analogy to Hamiltonian dynamical systems. In this colloquium I will describe a model for the dynamics of vortex filaments in a three dimensional fluid which are near-parallel. The talk will describe 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 L. Corsi (Georgia Institute of Technology), C.Garcia (UNAM) and C.-R. Yang (McMaster and the Fields Institute)
Der Vortrag führt in allgemein verständlicher Weise ein in die Gleichungen von Navier-Stokes, berührt zentrale Fragestellungen zum Millenniumsproblem und endet mit neuen Ergebnissen zur Regularitätstheorie.