Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Department Colloquium


Oleg Bogoyavlenskij, Queen's University

Friday, September 7th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Oleg Bogoyavlenskij (Queen's University)

Title: Counterexamples to Moffatt’s statements on vortex knots

Abstract: One of the well-known problems of hydrodynamics is studied - the problem of classification of vortex knots for ideal fluid flows. In the literature there are known Moffatt's statements that all torus knots $K_{m,n}$ for all rational numbers $m/n$ $(0 < m/n < \infty)$ are realized as vortex knots for each one of the considered axisymmetric fluid flows. We prove that actually such a uniformity does not exist because it does not correspond to the facts. Namely, we derive a complete classification of all vortex knots realized for the fluid flows studied by Moffatt and demonstrate that the real structure of vortex knots is much more rich because the sets of mutualy non-isotopic vortex knots realized for different axisymmetric fluid flows are all different.