From: rockbrentwood@gmail.com   
      
   On Sunday, November 8, 2020 at 10:18:06 AM UTC-6, Jos Bergervoet wrote:   
      
   > The Navier-Stokes equations can be simplified in two ways:=20   
   > by putting to zero the compressibility and/or the viscosity,=20   
   > which then leaves us with 4 cases..=20   
      
   I won't repeat what was said in an earlier reply (about surveying the   
   field before jumping in), but will note a few things. The best way to   
   address the problem is to remove the constraints and broaden it back out   
   to the simple and elegant form   
      
   d_t(rho) + del . (rho u) =3D 0   
   d_t(rho u) + del . (rho u u + P) =3D rho g   
   with constitutive laws   
   (d_t + u.del) rho =3D 0 - non-compressibility   
   P =3D (p - lambda del.V) I - mu (del u + (del u)^+) - the stress model   
   where I is the identity dyad, and P the stress tensor dyad   
      
   ... and to broaden it to include the *other* transport equations for the   
   other Noether 4-currents of the kinematic group. The 2 equations above   
   are the transport equations for mass and momentum. The kinematic group -   
   the Bargmann group - also has kinetic energy, and *especially* angular   
   momentum and moment. These transport equations should also be included   
   and the whole system dealt with in its entirety ... especially the   
   equations for angular momentum, because this figures prominently in the   
   actual fluid dynamics that come out of the Navier-Stokes equation!   
      
   You want to make money on this, and that's your motivation? Rather than   
   just that of advancing science and mathematical physics? Well, then you   
   had better hurry. Because if we solve it first, we're *refusing* the   
   prize and nobody's going to get anything.   
      
   Moneyed interests have no place in science and mathematics and   
   Perelman's precedent will be honored and continued.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)