Measure Attractors For Stochastic Navier-Stokes Equations

: We show existence of measure attractors for 2-D stochastic Navier-Stokes equations with general multiplicative noise. Keywords: Stochastic Navier--Stokes equations, measure attractors AMS subject classification: Primary: 35Q30, 60H15, 60G60; Secondary: 35R60, 76D05, 60J25 The research of the first author was supported by an EPSRC Visiting Fellowship at the University of Hull and also partially by the KBN grant 2PO3A 064 08. Submitted to EJP on 15 May, 1997. Final version accepted on May 20, 1998. MEASURE ATTRACTORS FOR STOCHASTIC NAVIER--STOKES EQUATIONS MAREK CAPI ' NSKI AND NIGEL J. CUTLAND Abstract. We show existence of measure attractors for 2-D stochastic Navier-Stokes equations with general multiplicative noise. 1. Introduction This paper is concerned with existence of attractors in connection with stochastic Navier-Stokes equations in dimension 2. For deterministic Navier-Stokes equations, the existence of a global attractor in dimension 2 goes back to the work of Ladyzh..