Stochastic Landau-Lifshitz equation. (English) Zbl 1240.60185

Guo, Boling; Pu, Xueke

Differ. Integral Equ. 22, No. 3-4, 251-274 (2009).

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.

Reviewer: Jana Šnupárková (Praha)

MSC:

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

Keywords:

stochastic Landau-Lifshitz equation; global weak solution; Stratonovich stochastic integral