Mathematical analysis

Hausdorff space

Vorticity

Navier–Stokes equations

Hausdorff measure

Engineering

Artificial intelligence

Physics

Hausdorff distance

Fractal dimension

Uniqueness

Dimension (graph theory)

Aerospace engineering

Integrable system

Pure mathematics

Mathematics

Class (philosophy)

Compressibility

Vortex

Computer science

Minkowski–Bouligand dimension

Hausdorff dimension

Bounded function

Fractal

Thermodynamics

Journal of the European Mathematical Society

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.

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