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Martingale solutions for stochastic Navier-Stokes equations driven by Lévy noise. (English) Zbl 1260.35128
Summary: In this paper, we establish the solvability of martingale solutions for the stochastic Navier-Stokes equations with Itô-Lévy noise in bounded and unbounded domains in \(\mathbb{R}^d, d = 2, 3\). The tightness criteria for the laws of a sequence of semimartingales is obtained from a theorem of Rebolledo as formulated by Metivier for the Lusin space valued processes. The existence of martingale solutions (in the sense of Stroock and Varadhan) relies on a generalization of Minty-Browder technique to stochastic case obtained from the local monotonicity of the drift term.

MSC:
35Q30 Navier-Stokes equations
60G44 Martingales with continuous parameter
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G15 Gaussian processes
60J75 Jump processes (MSC2010)
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