Martingale and Pathwise Solutions to the Stochastic Zakharov-Kuznetsov Equation with Multiplicative Noise

2013/07/25 by Nathan Glatt-Holtz, Roger Témam, Glatt-Holtz, Nathan +4
Economics, Econometrics and Finance · Mathematics · #35Q35 #60H15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stochastic processes and financial applications #math.AP #msc:35Q35 #msc:60H15

paper · pdf · doi:10.48550/arxiv.1307.6803

arxiv created 2013/07/25 · openalex publication_date 2013/07/25 · arxiv updated 2013/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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