Mathematician James Glimm may have solved the Poincare Conjecture
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Re: Mathematician James Glimm may have solved the Poincare Conjecture
#2The 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 https://arxiv.org/pdf/2212.14734.pdf
Re: Mathematician James Glimm may have solved the Poincare Conjecture
#3The 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 https://arxiv.org/pdf/2212.14734.pdf
Non pdf abstract: https://arxiv.org/abs/2212.14734
Re: Mathematician James Glimm may have solved the Poincare Conjecture
#4The 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.
[0] https://www.wired.com/story/a-new-computer-proof-blows-up-ce...