A stochastic Navier-Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure µν whose covariance is given in terms of the enstrophy. Pathwise uniqueness for µν-a.e. initial velocity is proven for solutions having µν as invariant measure.
We deal with the 3D inviscid Leray-α model. The well posedness for this problem is not known; by adding a random perturbation we prove that there exists a unique (in law) global solution. The random forcing term formally preserves conservation of energy. The result holds for initial velocity of finite energy and the solution has finite energy a.s.. These results are easily extended to the 2D case.MSC2010: 35Q31, 60H15, 35Q35.
Dedicated to Professor Boles law Szafirski on his 80th birthday.Abstract. We consider the Navier-Stokes equations in R d (d = 2, 3) with a stochastic forcing term which is white noise in time and coloured in space; the spatial covariance of the noise is not too regular, so Itô calculus cannot be applied in the space of finite energy vector fields. We prove existence of weak solutions for d = 2, 3 and pathwise uniqueness for d = 2.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.