Seminar at SMU Delhi

In this talk, we discuss the solvability of martingale problem for the stochastic Navier-Stokes equations with Itō-Lévy noise under appropriate conditions in bounded and unbounded domains in $R^d, d = 2, 3$. 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 Minty stochastic lemma which is essentially obtained from a local monotonicity of the drift term.