Strong solutions of the Landau-Lifshitz-Bloch equation in Besov space

2022/11/06 by Peng, Yi, Wang, Huaqiao
#35D35 #35K10 #35K59 #82D40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.03056

Abstract

We focus on the existence and uniqueness of the three-dimensional Landau-Lifshitz-Bloch equation supplemented with the initial data in Besov space B_2,1^(3)/(2). Utilizing a new commutator estimate, we establish the local existence and uniqueness of strong solutions for any initial data in B_2,1^(3)/(2). When the initial data is small enough in B_2,1^(3)/(2), we obtain the global existence and uniqueness. Furthermore, we also establish a blow-up criterion of the solution to the Landau-Lifshitz-Bloch equation and then we prove the global existence of strong solutions in Sobolev space under a new condition based on the blow-up criterion.

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