I don’t think this problem is very relevant. The Millennium Problem only asks about the smoothness of solutions to the incompressible Navier-Stokes equations. R

I don’t think this problem is very relevant. The Millennium Problem only asks about the smoothness of solutions to the incompressible Navier-Stokes equations. Real fluids are compressible and also conduct heat. In other words, if you solve the problem, you only learn how fluids behave under unrealistic assumptions. Physically speaking, one learns nothing from such mathematical exercises. Furthermore, singularities in the velocity field essentially imply velocities greater than the speed of light. That, too, is physically nonsensical, as we know from the theory of relativity. In other words, the solution only tells us that the incompressible Navier-Stokes equations are not realistic. But physicists have known that for a long time.