A new topological bound for energy of fluid flows

Geometry Topology Seminar
Friday, October 24, 2008 - 14:00
1 hour (actually 50 minutes)
Skiles 269
University of Pennsylvania
In many physical situations we are interested in topological lower bounds for L^2-energy of volume preserving vector fields. Such situations include for instance evolution of a magnetic field in ideal magnetohydrodynamics. Classical energy bounds involve topological invariants like helicity which measure linkage of orbits in the flow. In this talk I will present a new lower bound in terms of the third order helicity, which is an invariant measuring a third order linkage of orbits. I will also discuss how the third order helicity can be derived from the Milnor's \mu-bar invariant for 3-component links.