The magnetization ripple: a nonlocal stochastic PDE perspective
Abstract
The magnetization ripple is a microstructure formed by the magnetization in a thinfilm ferromagnet. It is triggered by the random orientation of the grains in the polycrystalline material. In an approximation of the micromagnetic model, which is sketched in this paper, this leads to a nonlocal (and strongly anisotropic) elliptic equation in two dimensions with white noise as a right hand side. However, like in singular Stochastic PDE, this right hand side is too rough for the nonlinearity in the equation. In order to develop a smalldate wellposedness theory, we take inspiration from the recent roughpath approach to singular SPDE. To this aim, we develop a Schauder theory for the nonstandard symbol $k_1^3+k_2^2$.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 DOI:
 10.48550/arXiv.1709.01374
 arXiv:
 arXiv:1709.01374
 Bibcode:
 2017arXiv170901374I
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Probability;
 35R60;
 35J60;
 78A30;
 82D40