This paper reviews the problems and successes of computing turbulent flow. Most of the flow
phenomena that are important to modern technology involve turbulence. The review is …

Incompressible flow problems appear in many models of physical processes and
applications. Their numerical simulation requires in particular a spatial discretization. Finite …

This book aims to bridge the gap between practising mathematicians and the practitioners of
turbulence theory. It presents the mathematical theory of turbulence to engineers and …

We review the properties of the nonlinearly dispersive Navier–Stokes-alpha (NS-α) model of
incompressible fluid turbulence—also called the viscous Camassa–Holm equations in the …

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 …

In this paper we discuss recent progress in using the Camassa–Holm equations to model
turbulent flows. The Camassa–Holm equations, given their special geometric and physical …

In this paper we present analytical studies of three-dimensional viscous and inviscid
simplified Bardina turbulence models with periodic boundary conditions. The global …

The first half of Onsager's conjecture states that the Euler equations of an ideal
incompressible fluid conserve energy if u (⋅, t)∈ C 0, θ (T 3) with θ> 1 3. In this paper, we …

We prove the global well–posedness and regularity of the (isotropic) Lagrangian averaged
Navier–Stokes (LANS–α) equations on a three–dimensional bounded domain with a smooth …