Stochastic hydrodynamic-type evolution equations driven by Lévy noise in 3D unbounded domains - abstract framework and applications

2013/06/22 by Elżbieta Motyl, Motyl, Elżbieta
Computer Science · Economics, Econometrics and Finance · Engineering · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1306.5342

openalex publication_date 2013/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The existence of martingale solutions of the hydrodynamic-type equations in 3D possibly unbounded domains is proved. The construction of the solution is based on the Faedo-Galerkin approximation. To overcome the difficulty related to the lack of the compactness of Sobolev embeddings in the case of unbounded domain we use certain Fréchet space. We use also compactness and tightness criteria in some nonmetrizable spaces and a version of the Skorokhod Theorem in non-metric spaces. The general framework is applied to the stochastic Navier-Stokes, magneto-hydrodynamic (MHD) and the Boussinesq equations.

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