A note on stochastic Navier-Stokes equations with not regular\n multiplicative noise

2015/10/13 by Zdzisław Brzeźniak, Brzezniak, Zdzislaw, Benedetta Ferrario +1
Economics, Econometrics and Finance · Mathematics · #60H15 #76D05 #76M35 #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1510.03561

openalex publication_date 2015/10/13 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We consider the Navier-Stokes equations in mathbb R^d (d=2,3) with a\nstochastic forcing term which is white noise in time and coloured in space; the\nspatial covariance of the noise is not too regular, so It ^o calculus cannot be\napplied in the space of finite energy vector fields. We prove existence of weak\nsolutions for d=2,3 and pathwise uniqueness for d=2.\n

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