Weak solutions of the Landau--Lifshitz--Bloch equation
Kim Ngan Le
TL;DR
This paper establishes the existence and regularity of weak solutions for the Landau--Lifshitz--Bloch equation at temperatures above the Curie point, providing foundational theoretical insights for high-temperature micromagnetics.
Contribution
It proves the existence of weak solutions for the LLB equation at high temperatures, addressing a gap in the rigorous mathematical theory of this model.
Findings
Existence of weak solutions for the LLB equation above Curie temperature
Discussion of regularity properties of these solutions
Foundation laid for further theoretical development
Abstract
The Landau--Lifshitz--Bloch (LLB) equation is a formulation of dynamic micromagnetics valid at all temperatures, treating both the transverse and longitudinal relaxation components important for high-temperature applications. We study LLB equation in case the temperature raised higher than the Curie temperature. The existence of weak solution is showed and its regularity properties are also discussed. In this way, we lay foundations for the rigorous theory of LLB equation that is currently not available.
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