Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

Abstract

We prove non-uniqueness for a class of weak solutions to the Navier-Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1.

31 pages, minor corrections, to appear in JEMS