Bounds on Kolmogorov spectra for the Navier-Stokes equations

► New estimate on the Fourier transform of weak solutions of the Navier-Stokes equations in 3D. ► Estimates on the spectral energy function E(κ). ► Upper bound on the decay rate E(κ); O(κ−2), a faster rate than the Kolmogorov law. ► Rigorous upper and lower bounds on the inertial range.