# American Institute of Mathematical Sciences

December  2012, 1(2): 355-392. doi: 10.3934/eect.2012.1.355

## Martingale solutions for stochastic Navier-Stokes equations driven by Lévy noise

 1 Center for Decision, Risk, Controls & Signals Intelligence, Naval Postgraduate School, Monterey, CA-93943, United States, United States

Received  July 2012 Revised  August 2012 Published  October 2012

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.
Citation: Kumarasamy Sakthivel, Sivaguru S. Sritharan. Martingale solutions for stochastic Navier-Stokes equations driven by Lévy noise. Evolution Equations & Control Theory, 2012, 1 (2) : 355-392. doi: 10.3934/eect.2012.1.355
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