C01 Singularity formation in dissipative harmonic flows

In this project we study the harmonic map heat flow equation and some of its variants, e.g., the Landau-Lifshitz-Gilbert equation. In these equations singularities are known to appear generically and spontaneously. Guided by analytical theory, we shall develop a reliable and flexible numerical simulation environment to capture singular phenomena based on tailor- made finite element methods. In return, numerical simulations will allow us to attack open mathematical questions regarding the singularity formation of harmonic flows in two and three space dimensions.

Project Leaders
Postdoctoral Researcher
Doctoral Researcher