Fluids, vortex sheets, and the skew mean curvature flow.

Series: 
School of Mathematics Colloquium
Thursday, April 19, 2012 - 11:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
IAS/University of Toronto
We show that the LIA approximation of the incompressible Euler equation describes the skew-mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for higher-dimensional vortex filaments  and vortex sheets as singular 2-forms with support of codimensions 2 and 1, respectively. This framework, in particular, allows one to define the symplectic structures on the spaces of vortex sheets.