  We consider the hypodissipative Navier-Stokes equations on
$[0,T]\times\mathbb{T}^{d}$ and seek to construct non-unique,
H\"older-continuous solutions with epochs of regularity (smooth almost
everywhere outside a small singular set in time), using convex integration
techniques. In particular, we give quantitative relationships between the power
of the fractional Laplacian, the dimension of the singular set, and the
regularity of the solution. In addition, we also generalize the usual vector
calculus arguments to higher dimensions with Lagrangian coordinates.
