On the Itô-Stratonovich Diffusion Limit for the Magnetic Field in a 3D Thin Domain
arxiv(2024)
摘要
We introduce a stochastic model for a passive magnetic field in a three
dimensional thin domain. The velocity field, white in time and modelling
phenomenologically a turbulent fluid, acts on the magnetic field as a
transport-stretching noise. We prove, in a quantitative way, that, in the
simultaneous scaling limit of the thickness of the thin layer and the
separation of scales, the mean on the thin direction of the magnetic field is
close to the solution of the equation of the magnetic field with additional
viscosity. In certain choice of noises with correlation between their
components and without mirror symmetry, we identify an Alpha effect.
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