On the regularity of solutions to the Navier-Stokes equations

A directional modulus of continuity is used to evaluate the scaling of each term in the incompressible Euler and Navier-Stokes equations. This is done by expressing the equations in terms of continuous Hermitian wavelets (derivatives of Gaussians), for which the exact scaling is easily derived. In the case of 3-D Euler with equal h's in all directions, runaway singularities are found for h < 1/3. In 2- and 3-D, it is found that the viscous term dominates for positive h's.