2D incompressible Navier-Stokes ain't too shabby. The problems they investigated should have been in the abstract. 3D compressible N.-S. where error is measure

2D incompressible Navier-Stokes ain't too shabby. The problems they investigated should have been in the abstract. 3D compressible N.-S. where error is measured via some functional of interest after direct numerical simulation of the discovered equations would be neat to see. I am curious which conservation laws it could figure out.