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

By El.zbieta Motyl. 2012

89 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/b7159619cdcdeca67eb5f1d7da96dd8cae5fd305

Citations in the corpus

• Stochastic Reaction-diffusion Equations Driven by Jump Processes (2010, unknown): “We finish the Introduction by pointing out that the approach presented in this paper (or rather it’s earlier arXiv version) has already been taken up and used for the proof of the existence of solutions to Stochastic Navier-Stokes equations and second grade fluids driven by Lévy noise, see [57] and ”