The stochastic Landau-Lifshitz-Baryakhtar equation in critical spaces

Abstract

We study the stochastic Landau--Lifshitz--Baryakhtar equation with multiplicative noise and homogeneous Neumann boundary conditions on smooth bounded domains in dimensions $d\le 3$. Relying on stochastic maximal regularity results, we establish global well-posedness in a variational strong, intermediate, and weak setting, as well as for initial data in the scaling-critical Besov spaces $B^{d/q-1}_{q,p}$ for every $q\in[2,\infty)$ and $p\in(2,\infty)$.