In this paper, we study the random data problem for incompressible
Navier-Stokes equations in Euclidean space. We prove that for any sβR, the almost sure local well-posedness holds in Hs(Rd)
when dβ₯2, and the almost sure global well-posedness holds in
Hs(R2). Our results have no regularity restriction, and thus can
cover arbitrary rough data.Comment: 19 page