Statistical properties of solutions to the Navier-Stokes equation in the limit of vanishing viscosity

Presents a new approach to the Navier-Stokes turbulence. With the Gaussian soft constraint on the Navier-Stokes equation, the author derives the energy spectrum to be E(k) approximately k^-3 and k^-2 in two and three spatial dimensions respectively. The possible future developments are also pointed out

Some ideas on the freely decaying Navier-Stokes turbulence

The author formulates a new approach to the Navier-Stokes turbulence. By analogy with Wilson's theory of critical phenomena, he tries to identify the upper critical dimension of the freely decaying Navier-Stokes turbulence. He points out the possibility of many fixed points. He also points out possible future developments