Potential Analysis

, Volume 38, Issue 3, pp 863–912 | Cite as

Stochastic Navier–Stokes Equations Driven by Lévy Noise in Unbounded 3D Domains

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Abstract

Martingale solutions of the stochastic Navier–Stokes equations in 2D and 3D possibly unbounded domains, driven by the Lévy noise consisting of the compensated time homogeneous Poisson random measure and the Wiener process are considered. Using the classical Faedo–Galerkin approximation and the compactness method we prove existence of a martingale solution. We prove also the compactness and tightness criteria in a certain space contained in some spaces of càdlàg functions, weakly càdlàg functions and some Fréchet spaces. Moreover, we use a version of the Skorokhod Embedding Theorem for nonmetric spaces.

Keywords

Stochastic Navier–Stokes equations Martingale solution Poisson random measure Compactness method 

Mathematics Subject Classifications (2010)

35Q30 60H15 76M35 

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computer SciencesLodz UniversityŁódźPoland

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