TITLE: Has it been proved that weak solutions to the Navier-Stokes equations are non-unique, and does this prove that the Navier-Stokes are not valid?
QUESTION [13 upvotes]: This preprint claims that, for finite kinetic energy initial solutions, uniqueness of weak solutions to the Navier-Stokes equations doesn't hold:
https://arxiv.org/abs/1709.10033
What's the current consensus of the community? Is the proof considered to be correct? Does this imply that the Navier-Stokes equations are not a valid model of fluid flow, or do we need a similar result for the smooth solutions of NS before we have to abandon/modify them?

REPLY [10 votes]: To avoid people finding this question via google and wondering about the correctness of this paper, I want to point out that the paper has now been accepted by the Annals; see here.