Organisation or Chair: RNDr. Šárka Nečasová, CSc. : Doc. Mgr. Milan Pokorný, Ph.D.
Submitted by:
Last update 11/10/12 15:14
Description
09:00 Speaker: Christof Melcher, RTWH Aachen
Title: Well-posedness of the Landau-Lifshitz-Gilbert equation
Abstract:
The Landau-Lifshitz-Gilbert equation is the fundamental evolution law in ferromagnetism. Mathematically, it appears as a hybrid between the heat and Schroedinger flow for harmonic maps. This combination of Hamiltonian and gradient flow structure gives rise to a number of interesting phenomena, but makes the analysis of this quasilinear evolution equation notoriously difficult. It is well-known that geometric PDEs of this kind may form singularities in finite time. This talk is concerned with questions of regularity. We shall introduce the method of moving frames that produces a gauged Ginzburg-Landau equation. Borrowing techniques previously used for semilinear equations, such as the Navier-Stokes equation, we prove a new global regularity result which is valid under a smallness condition on the initial date in terms of a critical Sobolev norm.
CZ
