Martingale and Pathwise Solutions to the Stochastic Zakharov-Kuznetsov Equation with Multiplicative Noise
Analysis of PDEs
2013-07-26 v1
Abstract
We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global pathwise uniqueness and the existence of pathwise solutions. New methods are employed in the passage to the limit on a special type of boundary conditions and in the verification of the pathwise uniqueness of martingale solutions with a lack of regularity, where both difficulties arise due to the partly hyperbolic feature of the model.
Keywords
Cite
@article{arxiv.1307.6803,
title = {Martingale and Pathwise Solutions to the Stochastic Zakharov-Kuznetsov Equation with Multiplicative Noise},
author = {Nathan Glatt-Holtz and Roger Temam and Chuntian Wang},
journal= {arXiv preprint arXiv:1307.6803},
year = {2013}
}