Existence of a martingale solution of the stochastic Navier-Stokes\n equations in unbounded 2D and 3D-domains

2012/08/16 by Zdzisław Brzeźniak, Brzeźniak, Zdzisław, Elżbieta Motyl +1 · 7 citations
Computer Science · Economics, Econometrics and Finance · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1208.3386

openalex publication_date 2012/08/16 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28

Abstract

Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains\ndriven by a multiplicative Gaussian noise are considered. The noise term\ndepends on the unknown velocity and its spatial derivatives. The existence of a\nmartingale solution is proved. The construction of the solution is based on the\nclassical Faedo-Galerkin approximation, the compactness method and the\nJakubowski version of the Skorokhod Theorem for non-metric spaces. Moreover,\nsome compactness and tightness criteria in non-metric spaces are proved.\nCompactness results are based on a certain generalization of the classical\nDubinsky Theorem.\n

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