On the local well-posedness for the fractional Landau–Lifshitz–Gilbert equation

We study the local well-posedness of the initial value problem of the fractional Landau–Lifshitz–Gilbert equation. We prove that for each initial data in the function space H4+αH4+α, there exists a unique solution in the functional space C([0,T];H4+α)∩C1([0,T];Hα)C([0,T];H4+α)∩C1([0,T];Hα) for some T>0T>0. Among other techniques, choosing the fractional Sobolev space serves as a key ingredient to the proof.