Stochastic Landau-Lifshitz equation. (Q636986)

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.