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Evolution Equations and Control Theory (EECT)
 

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

Pages: 355 - 392, Volume 1, Issue 2, December 2012      doi:10.3934/eect.2012.1.355

 
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Kumarasamy Sakthivel - Center for Decision, Risk, Controls & Signals Intelligence, Naval Postgraduate School, Monterey, CA-93943, United States (email)
Sivaguru S. Sritharan - Center for Decision, Risk, Controls & Signals Intelligence, Naval Postgraduate School, Monterey, CA-93943, United States (email)

Abstract: 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.

Keywords:  Stochastic Navier-Stokes equations, martingale solutions, Lévy noise.
Mathematics Subject Classification:  35Q30, 60G44, 60H15, 60G15, 60J75.

Received: July 2012;      Revised: August 2012;      Available Online: October 2012.

 References