Martingale solutions for stochastic Navier–Stokes equations driven by Lévy noise
Sritharan, Sivaguru S.
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In this paper, we establish the solvability of martingale solutions for the stochastic Navier-Stokes equations with Itˆo-L ́evy noise in bounded and unbounded domains in Rd,d = 2,3. The tightness criteria for the laws of a sequence of semimartingales is obtained from a theorem of Rebolledo as for- mulated by Metivier for the Lusin space valued processes. The existence of martingale solutions (in the sense of Stroock and Varadhan) relies on a gen- eralization of Minty-Browder technique to stochastic case obtained from the local monotonicity of the drift term.
The article of record as published may be found at http://dx.doi.org/10.3934/eect.2012.1.355
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