The Poincaré conjecture was solved by Grigory Perelman in 2006, this article is about James Glimm's solution of the Navier-Stokes Equation - see the paper at <a href="https://arxiv.org/pdf/2212.14734.pdf" rel="nofollow">https://arxiv.org/pdf/2212.14734.pdf</a>
The mathematics in this article looks not all that complex. From the little that I understand about it, it is not a direct proof that the equations are stable, but that it is based on a definition of enthropy and a stochastic argument. That argument gives good reasons to assume that the equations are smooth, but I wonder if it proofs that it is smooth in all cases. In this regard, it is interesting to note that in a recent paper [0] it was shown that Euler equations (a simpler system than the Navier-Stokes equations) might be instable.<p>[0] <a href="https://www.wired.com/story/a-new-computer-proof-blows-up-centuries-old-fluid-equations/" rel="nofollow">https://www.wired.com/story/a-new-computer-proof-blows-up-ce...</a>