Existence, uniqueness and regularity of solutions to the stochastic Landau-Lifshitz-Slonczewski equation

Beniamin Goldys, Chunxi Jiao and Kim Ngan Le

Abstract

In this paper we are concerned with the stochastic Landau-Lifshitz-Slonczewski equation (LLS) that describes magnetisation of an infinite nanowire evolving under current driven spin torque. The current brings into the system a multiplicative gradient noise that appears as a transport term in the equation. We prove the existence, uniqueness and regularity of pathwise solutions to the equation.

Keywords: nanowire, spin transfer torque, stochastic Landau-Lifshitz-Slonczewski equation, transport noise, pathwise solutions.

AMS Subject Classification: Primary 35D30; secondary 35K55, 35K59, 35Q49, 35Q60, 60H15.