Martingale solutions for stochastic Navier-Stokes equations driven by Lévy noise. (English) Zbl 1260.35128

Sakthivel, Kumarasamy; Sritharan, Sivaguru S.

Evol. Equ. Control Theory 1, No. 2, 355-392 (2012).

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)

Keywords:

stochastic Navier-Stokes equations; martingale solutions; Lévy noise