Potential Analysis

, Volume 38, Issue 3, pp 863-912

First online:

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

  • Elżbieta MotylAffiliated withDepartment of Mathematics and Computer Sciences, Lodz University Email author 


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.


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

Mathematics Subject Classifications (2010)

35Q30 60H15 76M35