Weak Solutions of a Stochastic Landau-Lifshitz-Gilbert Equation Driven by Pure Jump Noise: Stochastic Landau-Lifshitz-Gilbert Equation Driven by Pure Jump Noise

TY - JOUR

T1 - Weak Solutions of a Stochastic Landau-Lifshitz-Gilbert Equation Driven by Pure Jump Noise

T2 - Stochastic Landau-Lifshitz-Gilbert Equation Driven by Pure Jump Noise

AU - Brzezniak, Zdzislaw

AU - Manna, Utpal

N1 - © Springer-Verlag GmbH Germany, part of Springer Nature 2019. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2019/2/15

Y1 - 2019/2/15

N2 - In this work we study a stochastic three-dimensional Landau-Lifschitz-Gilbert equation perturbed by pure jump noise in the Marcus canonical form. We show existence of weak martingale solutions taking values in a three-dimensional sphere $\mathbb{S}^2$ and discuss certain regularity results. The construction of the solution is based on the classical Faedo-Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces.

AB - In this work we study a stochastic three-dimensional Landau-Lifschitz-Gilbert equation perturbed by pure jump noise in the Marcus canonical form. We show existence of weak martingale solutions taking values in a three-dimensional sphere $\mathbb{S}^2$ and discuss certain regularity results. The construction of the solution is based on the classical Faedo-Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces.

KW - Stochastic Landau-Lifshitz equation

KW - weak martingale solutions

KW - Marcus canonical form

KW - Lévy noise

U2 - 10.1007/s00220-019-03359-x

DO - 10.1007/s00220-019-03359-x

M3 - Article

SN - 0010-3616

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

ER -