We show that the pressure associated with a distributional solution of the Navier–Stokes
equations on the whole space satisfies a local expansion defined as a distribution if and …

This study introduces a new family of volumetric flatness factors which give a rigorous
parametric description of the phenomenon of intermittency in fully developed turbulent flows …

Recently, strong evidence has accumulated that some solutions to the Navier–Stokes
equations in physically meaningful classes are not unique. The primary purpose of this …

Many issues pioneered by Jackson Herring deal with how nonlinear interactions shape
atmospheric dynamics. In this context, we analyze new direct numerical simulations of …

Intermittency as it occurs in fast dynamos in the MHD framework is evaluated through the
examination of relations between normalized moments at third order (skewness S) and …

The question of whether a singularity can form in an initially regular flow, described by the
3D incompressible Navier–Stokes (NS) equations, is a fundamental problem in …

The problem of global-in-time regularity for the 3D Navier-Stokes equations, ie, the question
of whether a smooth flow can exhibit spontaneous formation of singularities, is a …

The problem of regularity and uniqueness are open for the supercritically dissipative surface
quasi-geostrophic equations in certain classes. In this note we examine the extent to which …

The goal of this paper is twofold. First, we give a simple proof that sufficiently sparse Navier–
Stokes solutions do not develop singularities. This provides an alternative to the approach of …

The goal of this note is to demonstrate that as soon as the hyper-diffusion exponent is
greater than one, a class of finite time blow-up scenarios consistent with the analytic …