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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 almosteverywhere outside a small singular set in time), using convex integrationtechniques. In particular, we give quantitative relationships between the powerof the fractional Laplacian, the dimension of the singular set, and theregularity of the solution. In addition, we also generalize the usual vectorcalculus arguments to higher dimensions with Lagrangian coordinates.

Epochs of regularity for wild H\"older-continuous solutions of the Hypodissipative Navier-Stokes System