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Stochastic hydrodynamic-type evolution equations driven by Lévy noise in 3D unbounded domains – abstract framework and applications. (English) Zbl 1303.35075
The author studies the existence of martingale solutions of the hydrodynamic-type equations in 3D possibly unbounded domains. The construction of the solution is based on the Faedo-Galerkin approximation. In order to master the difficulties connected with the lack of compactness of Sobolev embeddings in the case of unbounded domains the author works with certain Frechet spaces. Furthermore, she uses compactness and tightness criteria in some nonmetrizable spaces and a version of the Skorohod theorem in non-metric spaces. The general solution scheme is then applied to some particular cases such as stochastic Navier-Stokes, magneto-hydrodynamic (MHD) and the Boussinesq equations. The paper is very comprehensive. All details are explained, sometimes in appendices.

MSC:
35Q35 PDEs in connection with fluid mechanics
35Q30 Navier-Stokes equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76M35 Stochastic analysis applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
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