## Naše akce - Seminář SIAM SC - Další akce

### Malte Kampschulte - Gradient flows in the framework of (Cartesian) Currents

Kdy: 09/12/2014 14:00

Kde: Seminární místnost KNM

When considering variational problems and PDEs where the function

only takes values on a fixed manifold, for example magnetization as

a unit-vector field, one often encounters topological singularities

which are nontrivial to handle using standard methods. The framework

of Cartesian Currents as introduced by Giaquinta, Modica and Soucek

is well suited to describe those singularities in static variational

problems. However it would be desirable to use this powerful tool to

also describe the singularity formation in dynamic problems, e.g.

the bubbling in the harmonic map heat flow or vortex annihilation in

micromagnetics. One step in this direction is looking at gradient

flows of Currents. For this, a surprisingly general all-time

existence result can be derived using minimizing movements.

Additionally I will present a generalization of the Wasserstein

distance which seems to be the right a candidate for a possible

metric on (Cartesian) Currents, being sensitive to topological

changes, but still resulting in the correct gradient flow.