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Stochastic Navier-Stokes equations driven by Lévy noise in unbounded 3D domains. (English) Zbl 1282.35282
Summary: 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.

MSC:
35Q30 Navier-Stokes equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76M35 Stochastic analysis applied to problems in fluid mechanics
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