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 $B_{q,p}^{d/q-1}$ for every $q\in [2,\infty )$ and $p\in (2,\infty )$.

Contribution to the Oberwolfach Report for the Seminar 'Stochastic Partial Differential Equations in Critical Spaces' organized by Antonio Agresti and Mark Veraar. Comments are welcome!