Stochastic Landau-Lifshitz equation. (English) Zbl 1240.60185

The Cauchy problem for the stochastic Landau-Lifshitz equation is studied. The authors consider a stochastic multiplicative noise and explain why the Stratonovich stochastic integral with respect to a standard Wiener process is appropriate. The existence of a global weak solution in the PDE-sense is proved in any \(\mathbb {R}^{d}\) using a discretization method. Moreover, when \(d=1\) the authors prove that the equation admits a global unique continuous solution showing at first that there exists a local in time solution to the periodic approximating equation.


60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35Q60 PDEs in connection with optics and electromagnetic theory
35R60 PDEs with randomness, stochastic partial differential equations