  Using the convex integration technique for the three-dimensional
Navier-Stokes equations introduced by T. Buckmaster and V. Vicol, it is shown
the existence of non-unique weak solutions for the 3D Navier-Stokes equations
with fractional hyperviscosity $(-\Delta)^{\theta}$, whenever the exponent
$\theta$ is less than J.-L. Lions' exponent $5/4$, i.e., when $\theta < 5/4$.
