Some thoughts on the Navier-Stokes news from a professor of aerospace engineering: 1) take a deep breath 2) posts indicating we "solved Navier-Stokes" are incorrect and overblown. A very specific mathematical proof involving a niche scenario for Navier-Stokes has *potentially* been shown (that a perfectly smooth incompressible initial condition with finite energy could produce a singularity--note the assumptions here piled on to an equation set that already involves some assumptions). 3) there is no general closed form solution for N-S and that's not what this news is about 4) this is more of a mathematical curiosity than anything else and could matter a lot to mathematicians but basically changes nothing in the way N-S are used in practice 5) there are already very useful exact solutions to Navier-Stokes that greatly simplify the equation set with the right boundary conditions/geometry like laminar flow through a pipe or a 2D Taylor-Green vortex 6) in aerospace, we already treat N-S as an approximation in many instances and are well aware of its limitations. we don't outright solve these equations anyway and regularly chop off terms or simplify parts (at the expense of accuracy) to make them easier to deal with. 7) to be honest I have never found this specific problem to be particularly interesting because we know a core assumption of N-S is a "continuum" fluid where you ignore molecules and assume hydrodynamic scales >>> molecular scales. We know a real fluid cannot have infinite velocity or energy. But clearly you can push equations outside of their bound of validity and make them produce funky results and singularities.

Several comments asking me about Stoke Space What they are doing (regeneratively-cooled metallic heat shield using LH2) is pretty neat and has promise. I talk sometimes about how what SpaceX did with Falcon 9 was more of an "engineering problem" (taking proven mid-TRL technology and making it work on a real system) than the issues with Starship's heat shield that I see as more of a "physics problem" (depending on your definition of "rapid" reuse). Engineering problems can be solved with iterative design and brute force. Physics problems need true advances in science and technology. All that to say, IMO what Stoke is trying to solve is an engineering problem. With the right people, enough money, and enough time, I think it will work. Anytime your design relies this heavily on hydrogen you're inviting some (incredibly small) demons to the party, but alas, not my problem. I'd love more details on their ground testing at "higher heat loads" than what is experienced in flight. But last I heard they're targeting a launch test late this year? Looking forward to finding out...