Bounds on Kolmogorov spectra for the Navier - Stokes equations

Andrei Biryuk, Walter Craig

Let $u(x,t)$ be a (possibly weak) solution of the Navier - Stokes equations on all of ${\mathbb{R}}^3$, or on the torus ${\mathbb{R}}^3/{\mathbb{Z}}^3$. The {\it energy spectrum} of…