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math.AP2018
Global dissipative half-harmonic flows into spheres: small data in critical Sobolev spaces
Christof Melcher, Zisis N. Sakellaris
We establish global existence, uniqueness, regularity and long-time asymptotics of strong solutions to the half-harmonic heat flow and dissipative Landau-Lifshitz equation, valid f…
math.AP2011
Global Solvability of the Cauchy Problem for the Landau-Lifshitz-Gilbert Equation in Higher Dimensions
Christof Melcher
We prove existence, uniqueness and asymptotics of global smooth solutions for the Landau-Lifshitz-Gilbert equation in dimension , valid under a smallness condition of init…