The past few decades have seen dramatic progress in our understanding of solar interior
dynamics, prompted by the relatively new science of helioseismology and increasingly …

Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis
The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize …

The Computational Anatomy project is the morphome-scale study of shape and form, which
we model as an orbit under diffeomorphic group action. Metric comparison calculates the …

Implicit representations can provide simple descriptions of relatively complex shapes and
can in many cases be a good choice when designing stable shape processing algorithms …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

Interactions between waves and mean flows play a crucial role in understanding the long-
term aspects of atmospheric and oceanographic modelling. Indeed, our ability to predict …

Large eddy simulation (LES) is a method of scientific computation seeking to predict the
dynamics of organized structures in turbulent flows by approximating local, spatial averages …

Since the early part of the 20th century, it has been understood that the description of nature
at the subatomic scale requires quantum mechanics. In quantum mechanics, the position …

We show here the global, in time, regularity of the three dimensional viscous Camassa–
Holm (Navier–Stokes-alpha)(NS-α) equations. We also provide estimates, in terms of the …

In this paper we introduce and study a new model for three–dimensional turbulence, the
Leray–α model. This model is inspired by the Lagrangian averaged Navier–Stokes–α model …