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

- Series
- School of Mathematics Colloquium
- Time
- Thursday, April 19, 2012 - 11:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Boris Khesin – 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.