Fractal geometry of turbulence  NavierStokes equations and the Hausdorff dimension
Abstract
Two theorems on the role of the Hausdorff dimension in the flow of viscous incompressible fluids governed by NavierStokes equations are stated. The first theorem states that the set of moments when the liquid is turbulent in the Leray sense has a Hausdorff dimension equal at most to one half. The second theorem states that at any moment the fluid is turbulent, its singularities are encompassed by a set S whose dimension is at most a little greater than one.
 Publication:

Academie des Sciences Paris Comptes Rendus Serie Sciences Mathematiques
 Pub Date:
 January 1976
 Bibcode:
 1976CRASM.282..121S
 Keywords:

 Existence Theorems;
 Flow Theory;
 NavierStokes Equation;
 Topology;
 Turbulent Flow;
 Incompressible Fluids;
 Metric Space;
 Singularity (Mathematics);
 Viscous Fluids;
 Fluid Mechanics and Heat Transfer