Well-posedness for the fractional Landau–Lifshitz equation without Gilbert damping

The main purpose is to consider the well-posedness of the fractional Landau– Lifshitz equation without Gilbert damping. The local existence of classical solutions is obtained by combining Kato’s method and vanishing viscosity method, by carefully choosing the working space. Since this equation is st...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2013-03, Vol.46 (3-4), p.441-460
Main Authors: Pu, Xueke, Guo, Boling
Format: Article
Language:English
Subjects:
Analysis
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Commutators
Control
Criteria
Damping
Dimensional analysis
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Partial differential equations
Regularity
Systems Theory
Theoretical
Viscosity
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Summary:The main purpose is to consider the well-posedness of the fractional Landau– Lifshitz equation without Gilbert damping. The local existence of classical solutions is obtained by combining Kato’s method and vanishing viscosity method, by carefully choosing the working space. Since this equation is strongly degenerate and nonlocal and no regularizing effect is available, it is a challenging problem to extend this smooth solution to global. Instead, we give some regularity criteria to show that the solution is global if some additional regularity is assumed, which seems minimal in the sense of dimensional analysis. Finally, we introduce the commutator and show the global existence of weak solutions by vanishing viscosity method.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-011-0488-6