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.
- Prof. Dr. Christof Melcher
- RWTH Aachen University
- more information
- +49 241 80 94585
- melcher@math1.rwth-aachen.de
- homepage
- Prof. Dr. Arnold Reusken
- RWTH Aachen University
- more information
- +49 241 80 97972
- reusken@igpm.rwth-aachen.de
- homepage
- Kilian Koch
- RWTH Aachen University
- more information
- koch@math1.rwth-aachen.de
- Nam Anh Nguyen
- RWTH Aachen University
- more information
- +49 241 80 94870
- nguyen@igpm.rwth-aachen.de
Publications
Discretization error analysis for a radially symmetric harmonic map heat flow problem
Preprint 2025
Pathwise Solvability and Bubbling in 2D Stochastic Landau-Lifshitz-Gilbert Equations
Preprint 2025
Well-posedness of half-harmonic map heat flows for rough initial data
Preprint 2025
Error analysis for a Finite Element Discretization of a radially symmetric harmonic map heat flow problem
Preprint 2025
Stochastic Landau-Lifshitz-Gilbert equations for frustrated magnets under fluctuating currents
Preprint 2023