Abstract
In this paper we consider the existence and uniqueness of weak energy solutions to a stochastic 2-dimensional non-Lipschitz Navier–Stokes equation perturbed by the cylindrical Wiener process W ( t ) in a bounded or unbounded domain D with the smooth boundary ∂ D or D = R 2 : d X ( t ) = [ − ν A X ( t ) + B ( X ( t ) ) ] d t + f ( t , X ( t ) ) d t + g ( t , X ( t ) ) d W ( t ) , where A is the Stokes operator and f, g satisfy the non-Lipschitz condition.
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