Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D-domains
By Zdzisław Brzeźniak, El.zbieta Motyl. 2012
173 citations recorded by the source corpus.
Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise are considered. The noise term depends on the unknown velocity and its spatial derivatives. The existence of a martingale solution is proved. The construction of the solution is based on the classical Faedo-Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod Theorem for non-metric spaces. Moreover, some compactness and tightness criteria in non-metric spaces are proved. Compactness results are based on a certain generalization of the classical Dubinsky Theorem.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/10efde0f12f6627d76d2ef22f869a2cff33fbcba
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In Computational Theory and Mathematics
In Control and Systems Engineering
In Finance
Citations in the corpus
- Stochastic Navier–Stokes Equations Driven by Lévy Noise in Unbounded 3D Domains (2012, methodology): “We will use the following auxiliary result proven in [9].”